Because... history. "The government" isn't one single entity. The debt limit affects the treasury specifically. As Wikipedia explains.
Between 1788 and 1917 Congress would authorize each bond issue by the United States Treasury by passing a legislative act that approved the issue and the amount.
Congress basically gave up that fine-grained control (over each bond issue) only because of WWI. Thereafter only an overall limit was set. The number of votes to has change the limit varied over time since then. There were more votes after 1960, sometimes several per year, because both suspension of the limit and increases were done. In this perspective, Congress has exercised more control post 1960s, but still less than before 1917 when they were approving roughly each bond issue.
The story from Wikipedia is actually slightly oversimplified. According to a CRS report, around WWII there were more changes:
The Constitution grants Congress the power to borrow money on the credit of the United States—
one part of its power of the purse—and thus mandates that Congress exercise control over federal
debt. Control of debt policy provides Congress with one means of expressing views on
appropriate fiscal policies.
Before 1917 Congress typically controlled individual issues of debt. In September 1917, while
raising funds for the United States’ entry into World War I, Congress also imposed an aggregate
limit on federal debt in addition to individual issuance limits. Over time, Congress granted
Treasury Secretaries more leeway in debt management. In 1939, Congress agreed to impose an
aggregate limit that gave the U.S. Treasury authority to manage the structure of federal debt.
I suppose your real questions is why the US adopted this practice in 1788 and has kept it on one form or another. The 1788 question is probably better on history SE.
As for what's proposed as explanation in FrederikVds' answer... I'm not sure I buy it entirely, but there is a rough correlation between when detailed budgeting was introduced (1921) and when Congress gave up on approving each bond issue (1917):
The U.S. Constitution (Article I, section 9, clause 7) states that "No money shall be drawn from the Treasury, but in Consequence of Appropriations made by Law; and a regular Statement and Account of Receipts and Expenditures of all public Money shall be published from time to time."
Each year, the President of the United States submits a budget request to Congress for the following fiscal year as required by the Budget and Accounting Act of 1921.
So there was probably a transition from one form of fine-grained Congress control (bond based) to another (budget line-item based) around WWI.
According to one 1996 paper between 1917 and 1996 the federal debt limit had been raised or suspended 80 times (64 times between 1960 and 1996). According to a 2017 Reuters article, the precise number of such actions 1960-2017 was 79. I cannot easily verify what's claimed in FrederikVds' answer that there was a substantial period of (post-1917) time when Congress didn't have to approve at least annually such a measure. It's possible they had some gentlemen's agreement and auto-raised it, but there was a formal act more than once per year, on average, according to the statistics. The distinction seems to be that no separate vote took place, but a measure to raise or suspend the debt was included in some other larger bill when Democrats controlled the House:
The Gephardt Rule is a component of the overall House Rules that Democrats use when they control the chamber. When Republicans have been in the majority over the last 40 years, as they were from 1995 to 2007 and again from 2011 to 2019, the GOP repealed this rule and required separate votes on the debt limit. [...]
The Senate does not have its own version of the rule and therefore still requires 60 votes in order to advance a debt limit resolution.
The finer effects of the Gephardt Rule are detailed in a separate CRS report:
Under the former Gephardt rule, in 11 of the 31 years between 1980 and 2010, the rule was either
suspended (1988, 1990-1991, 1994-1997, and 1999-2000) or repealed (2001-2002) by the House.
In most years in which the rule was suspended, legislation changing the statutory limit was not
necessary—that is, at the time, the existing public debt limit was expected to be sufficient.
During the years in which the rule applied (i.e., in the 20 of the 31 years between 1980 and 2010),
the rule led to the automatic engrossment of 20 House joint resolutions increasing the statutory
limit on the public debt. In effect, under the rule, in these cases, the House was able to initiate
legislation increasing the level of the public debt limit without a separate, direct vote on the
legislation. Of these 20 joint resolutions, 15 became law. In 10 of these 15 cases, the Senate
passed the measure without change, allowing it to be sent to the President for his signature
without any further action by the House. In the remaining five cases, the Senate amended the
rule-initiated legislation, requiring the House to vote on the amended legislation before it could
be sent to the President.
During this period, the House also originated and considered debt limit legislation without
resorting to the Gephardt rule either as freestanding legislation, as part of another measure, or as
part of a budget reconciliation bill. Of the 47 public debt limit changes enacted into law during
the period 1980-2010, 32 were enacted without resorting to the Gephardt rule, each requiring the
House to vote on such legislation.
In total, between 1980 and 2010, the rule effectively allowed the House to avoid a separate, direct
vote on 10 of the 47 measures changing the debt limit that were ultimately enacted into law.
I didn't want to get into this as veering a fair bit from the main topic and also is a rather long story, but since people have follow-up questions (and the image painted in the other answer is rather terse):
When the US was formed it really had just a "congressional budget". The Treasury reported directly to Congress by the law passed soon thereafter. Government agencies that were eventually formed received their separate budgets each mainly drafted/approved by various Congressional committees that had little coordination with each other.
There was a substantial Progressives move toward 1900 to have an European-style executive budget in the US. One milestone was president Taft's proposal via a commission he appointed in 1911-12. These changes/proposals were under the banner (to paraphrase from later president Wilson's words) that Congressional committees had become the true ministers and that executive ministers were merely their clerks robbing the executive of most its powers. (Taft himself was apparently not incredibly sold on the idea, but he allowed the commission as a way to placate and gain support of the Progressive wing of the Republican party.)
Wilson wanted a hierarchically structured budget driven by one executive vision, but he actually wanted it on terms that Congress could not agree with. Congress sent him a version of the budget law that Wilson vetoed, seemingly because it didn't allow him to fire the comptroller. (This newly introduced [at federal level] post oversaw the newly created GAO which oversaw the auditing processes.) Wilson's successor, president Harding was more compromising in terms of the balance of powers; he was in fact a proponent of the version that passed during his presidency. The 1921 law was also a compromise in that it allowed Congress to amend the initial executive budget proposal.
The 1921 budget law still had issues it didn't fully address like impoundments (the executive's ability to not actually spend money that Congress allocated for a given purpose), which were still being solved on a gentlemen's agreement basis. That worked out until president Nixon started to massively [over]use impoundments to block most Congressional programs he disagreed with, impoundments reaching 17%-20% of the budget sum during his presidency. Although elected in a landslide, Nixon was forced to give this unilateral impoundment power by the 1974 act (passed over his veto) that made it necessary for a president to seek congressional approval for longer term impoundments, rather than brief suspensions. There were other changes made to the budgeting process made in that 1974 reform, like the introduction of reconciliation and the more technocratic CBO nominally controlled by the newly created Congressional budget committees, but given a fair bit of independence in practice.
These issues didn't squarely deal with the debt ceiling in any way, but were part of the big picture of budget process reform(s). During the debates on impoundment reform in the 1970s, the Nixon administration did try to paint Congress as "pro-spending" and itself as the more fiscally responsible part of the government, in a sense trying to create a mirror of the debate that on hears from Congress on the debt ceiling. The overall effects of the 1974 act on the balance of powers are still somewhat debated because reconciliation (which was also included in the act) gave the executive the ability to pass its budget with with a narrower majority in Congress (in the Senate in particular), which made the system closer in this regard to European budgeting processes. (Back in Taft commission's days, they were inspired by a Westminster style system in which the failure of a major budget proposal meant the dismissal of the government/executive; but this could not be squared with the US system of a separately elected president. The UK itself moved away from its historical model in 2011, when a law was adopted that makes government dismissal dependent on an explicit [no-]confidence vote, i.e. failure to pass a major budget proposal is no longer equated with automatic government dismissal.)
I wrote this part rather quickly so there won't be inline refs, but I've used these sources:
