It's a good idea if you think the President should have much stronger powers than other branches, and that legislative compromise should be eliminated, as part of the system, altogether.
As much as we hate the way legislation is bundled, it is, quite often the way to work compromise into the system. I don't vote for measure "A", but I want measure "B", which measure "A" proponents oppose. In both cases, our support for our causes outweighs the aversion for the others' proposal, so they get bundled together.
If the President has the power to pick off just the pieces he doesn't like, it subverts the intent of the legislation, and, some may argue, basically allows the President to craft legislation (since vetoes are incredibly difficult to override), which is supposed to be the power of Congress. Congress is supposed to write the laws, the president approves them and is in charge of execution of those laws. The President is not supposed to be able to write laws, and this fine editing, some argue, basically gives him/her that power.
If the party or parties not aligned with the President don't have veto-overriding majorities, then they know that anything they want stands a strong chance of being edited out, and then there's no reason for them to support or not obstruct items on the President or his party's agenda.
Also, keep in mind, in general, this gives the President huge, specific, granular power over crafting budgets and legislation. Just as parties within Congress generally have to bargain and compromise, so do the different branches of government. This power greatly skews the balance of power.
It's very easy to veto just a few items you don't like, but when the decision gets made on allowing your own desired initiatives to go through, but only if some opposition items are attached, then the use of the veto becomes much less frequent and only for "big deal" items. The norm is discussion and compromise when that is in place, which, probably, is what the Founders envisioned.
On a more abstract scale, the Founders created what is supposed to be, on the surface of it, three co-equal branches of government in this system of checks and balances. The branch that is addressed first in the Constitution is the Legislative branch. Some Constitutional scholars argue that this is intentional, and the Founders wanted Congress to be "first among equals." Giving the President that much power and leverage would undermine that intent.
Does Congress Want to Govern? | RealClearPolicy
There's a reason why founding father James Madison called Congress "the first branch" of government...... It's no accident that the legislative branch is described in Article I of the Constitution, or that Article I is longer than the other six articles, combined.
What is Congress? - Shmoop