Fetterman is a shtick artist worthy of the Vaudeville stage, and it's going to catch up to him someday.
Not only would Biden look terrible ("old man screams at a bunch of dumb college students"), there's also the fact that he's actually president. His actions have some influence over how events unfold. He can't just default to unconditionally backing Israel when even someone like Chuck Schumer is pushing for more nuance.
You ever heard of a Sista Soulja moment? It worked wonders for Bill Clinton. One of Biden's biggest flaws has been his unwillingness to call out the left flank of his party. It's plagued his entire administration from day one and now it's caught up to him. Far left politics are not popular and trying to placate to that fringe group has no upside to it.