Not only economy but also military equipment and manpower, it costs nigh nothing to the US - all the "donations" to Ukraine instantly come back as profits for American MIC.
Your analysis would be 100% true IF EU was always a "yes-man" for the US but prior to the war they started getting uppity - calls for EU army, refusal to drop NS-2, Huawei was not banned everywhere, etc. The incoming economic damage and future dependence on the US not only for defence but also for energy will squash that kind of dissent, EU will become a full-time US bitch even worse than Japan. The US keeps its "allies" strong enough but not too strong so that they can always quickly put them down if they start challenging them. Now that the EU is becoming dependent on the US in two crucial sectors while losing a lot of its industry (some of it also went to the US), it will be easier for the US to control them. I expect the incoming visits of Scholz & Macron to be complete waste of time.
US always had control over EU, they were just allowed token criticism in order to keep up a veneer of legitimacy. West Germany and NATO were built off of nazi officials that owe a life debt to US pardoning them. You really think these ex nazis and their successors had any agency in their decisions?
Only France is a bit more independent, but France is outnumbered by Germany and their puppet migrant worker states like Poland and Lithuania.
A dictator is strong when he allows criticism. Because he is so secure in the knowledge that he sits safe, controlled criticism can be allowed. When he is clamping down on any form of dissent, no matter how small, that shows weakness. The worst crackdowns happen right before he is overthrown.
What I'm saying is, things are getting worse now in EU, but it is better for EU because before things get good, things need to get worse.
And this is not a desirable outcome for America. It is much better to have an Europe with industry, ability to innovate and well fed population that organically takes US side because they feel like the future is with America.
No dictator actually wants to clamp down on their subjects, and "Europe's last dictator" is no exception to that.