What if the ability of presidents to issue pardons was suspended from, say, October 15 of a presidential election year through January 20 of the following year?

It would never happen (the Constitution would need to be amended), but it's an interesting thought experiment.

From the perspective of a potential "pardonee", there shouldn't be a big difference. A person who had the misfortune to have alleged misdeeds (or a criminal conviction - think Ted Stevens) come to light after October 15 of an election year might be out of luck, especially if the next president is of a different political party. But no one is entitled to get a pardon anyway.

From the perspective of the country, there would be, at least, a small way to register disapproval with a president's use of the pardon power. Of course, it's not ideal - a president probably would still save the most controversial pardons for the year in which she or he was not up for re-election. So the voters would have only the option of voting against the nominee of the president's party if the voters disapproved of the pardon.

But even that potential consequence might deter presidents from some pardons that might be issued otherwise. Not the most pressing issue around, but a good time to think about it given the pardons that the current (otherwise absentee) president will likely issue between now and January 20.