"Rival" power is a matter of choice though, isn't it? The EU could as easily have chosen to align with Russia as with they've done with the US. In the same way that both France and Germany are powers but they're not really rival. EU should have gone its own way after 1991, NATO stopped making sense after the communist block was dissolved, and the fact that it kept growing and moving further towards the east in violation of the agreements reached last century, kinda shows that it's not a defensive alliance as much as it is subservience to US's geopolitical interests.

This isn't to say the EU should be aligned to Russia or that the war in Ukraine isn't primarily Putin's fault, or that there shouldn't be a military alliance in Europe, I'm just saying the US shouldn't belong to it, let alone dictate its terms.