Degrading the Russian military through a proxy war is the cheapest and safest way to defend our NATO allies in Eastern Europe. Regardless of whether Russia eventually wins or loses in Ukraine, their military capabilities are being shattered and will take decades to rebuild.
It is incredibly cheap in terms of dollars spent by NATO to kneecap the Russian military and prevent future expansion.
The US spent trillions for decades preparing for this sort of fight, all the way up to Ronald Reagan’s Star Wars stuff… and it turned out that something like 20% of one year’s US military budget (and some very brave, determined allies) does the trick.
Cheap for the USA. It's for the Ukrainians to decide whether the cost in lives is worth paying. As long as they're willing to keep fighting there's no downside for us in supplying weapons.