Putin has been sabre rattling since the war started, when he found occupying Ukraine was not a walk over. I do not think Biden had any choice but to let Ukraine use its missiles over Russia.
Trump is prepared to sell Ukraine down the river in his pursuit of an isolationist USA. Ukraine needs all the bargaining chips it can get ahead of that - and doing serious damamge to Russia and occupying Russian territory is an important part of that strategy. There are also a buffer of states on Ukraine's borders: Moldova, Georgia, even Poland, who fear that given free rein Putin will want to add them to his empire. They look to the free world, which includes NATO, as a military organisation, and the EU, as a political organisation as their protection and while, I agree, that NATO needs to be less reliant on the Americans, than it is, but at the moment those border states need reassurance. It is not coincidence that after Putin invaded Ukraine, that a group of states previously resolutely neutral in Europe: Finland and Sweden among them, promptly applied to join NATO.