The EU has no real reliance on US military might. Russia has been shown to be a paper tiger and the EU can use Ukraine as a proxy to cripple Russia while keeping their hands relatively clean.

The EU would strongly prefer to have US military support, but does not fundamentally need it. In the miltiary domain, but also lots of other domains, the EU is using these fake promises they made to Trump as a mechanism to buy time while they quietly work on removing US dependencies, and reducing US leverage.

For what? Defense against Russia?

I suspect that if my country gave Putin what we give to the US - military bases where they can do whatever they please no questions asked, real-time intelligence access, unofficial favored supplier status for anything that might be control-relevant, quiet veto power over any national policy decision deemed "strategic" - then we wouldn't have to worry about invasion - from Russia anyway. Why invade what you already own?

I think that price is a little too steep, though. Not to mention that the US would then be at least as willing to topple governments/invade as Russia currently is.