It's not actually two-and-a-half months
The President is not elected early-November, but mid-December by the Electoral College.
This is similar to parliaments who choose a prime minister. As extreme examples, Belgium went 18 months without a PM in 2010. Spain went without a PM for 7 months last year.
Practically, the future US President is usually known soon after the November election. However, this is only a consequence of the de facto two-party system present in the US, not a legal condition. Were the US to have several significant parties like Belgium or Spain, similar events with the would occur.
And in fact the US has had a contingent (non-majority) Presidential election twice: 1800 and 1824. The election went to House for additional voting. The former event required thirty-five rounds of voting by the House to resolve.
The significant factor is the fixed date
Countries with a fixed inaguration date place election a ways before it. As another answer mentioned, the Dominican Republic has fixed inaguration dates, with a similar delay between it and the election.
Most democracies don't have constitutionally-fixed dates. (This is why governments were able to delay elections for the pandemic; imagine the crisis if Trump attempted a similar action.)
If you have a fixed inaquration date, there is really no choice but to separate them by some time. Consider the protracted court battle in 2000 that wasn't resolved until over a month after the popular vote. Or consider recent judicial rulings that US states must count mail-in ballots weeks after election day.
Under those circumstances, it'd be extremely risky to hold election only a few weeks between the required transition of power. You'd be only one sticky situation away from a constitutional crisis.