I can’t believe this needs to be said, but: Trump has exposed some weaknesses in institutions, but those weaknesses have been

A) A power granted to the President that had not previously been used like so, or
B) A process he could slow or stop by refusing to cooperate

The transfer of power between presidents is neither of these things. He doesn’t have the power to say ‘I’m still the President’, and there’s no part of the process that requires his cooperation or consent.

If he sits in the White House watching Fox and rage tweeting and refusing to leave in Jan 2021, he still stops being President (god willing and the creek don’t rise).

If he actively attempts to stay in power, that’s called a coup. It would require the cooperation of the military and federal law enforcement. It’s also vanishingly unlikely for a number of reasons.

For one thing, he’s not particularly well loved by the military, and especially not the officer class. But on a more basic level, it’s a lot of work and he’s lazy and doesn’t seem to particularly like the job in the first place.

If he does attempt a coup, that’ll be a scary time for America, even if it doesn’t work (and I suspect it wouldn’t). But the fantasy that he’ll just say ‘nah I’m President’ and everyone will just go along with it is ridiculous.