President Biden may have expressed a wish to run, but he needs the nomination and backing of his party to do so, neither of which I would imagine will be forthcming.
What you want, and what you can have very often two different things.
Well I think as the incumbent president there's evey chance he will get the backing of his party.
I am in two minds about this: I am a fan of Biden but by the end of his second term he'd be 85/86 which is, y'know, knocking on a bit.
He deserves a longer retirement.