I think the US is fine with another destroyed state in eastern Europe. Both Russia and the EU will have to deal with the refugee crisis caused by prolonging this war, but as we've seen with the attack on Nord Stream, the US is happy to economically sabotage the EU if it also hurts Russia. The US doesn't need Ukraine to be capable of supporting a population or economic activity in order to stage weapons there, and I think that's why the longer the US artificially prolongs the war, the more Russia's going to feel that taking control of the entire territory is the only way to prevent that from happening.

Counter to the US line that Russia always intended to annex Ukraine (and then the rest of Europe), I think Russia tried very hard for years to maintain a status quo where Ukraine was neutral and independent, but also not creating a refugee crisis in the Donbass and staging NATO resources on the Russian border. When the Donbass republics seceded and the Ukrainian regime and their handlers made clear they wouldn't stop accelerating the provocations, I think Russia felt that directly securing the Donbass would eventually force the Ukrainian regime to the negotiating table.

As the US makes it more clear that they won't permit any negotiated end to the war, I think it's likely that the US is fine with the collapse of the current Ukrainian state as long as they can they can leave behind an ISIS-like group of Banderites launching terrorist attacks into Russia for the foreseeable future. NATO saying even now that Ukraine is too corrupt to join just reconfirms for me that preserving the Ukrainian state was never NATO's objective in orchestrating this war. That puts Russia in the position of having to either capture, rebuild, and administer the entire destroyed country in order to completely snuff out the Banderites, or risk a Syria-like situation on their border where NATO just waits for the Ukrainian government to collapse and starts directly setting up military bases in the west under the guise of "humanitarian peacekeeping" and "fighting terrorism".

It remains to be seen whether the empire actually has the economic resources to occupy Russia in a prolonged proxy war for years to come where also exterminating Palestine and preparing for an attack on China. I think there's obviously a strong case to be made that the US doesn't have that capacity, but nobody making imperial policy decisions would ever acknowledge that possibility.