If they did that, I hope they would coordinate the timing with America first. It would be American forces, not so much the EU, that would be helping Taiwan defend against the invasion that would probably follow.
So more than that I'd hope EU can then put its squabbling aside and respong in unison to any military provocation as well.
Source: https://en.wikipedia.org/wiki/List_of_aircraft_carriers_in_s...
In the EU we view the "Department of Defense" as a tool for actual defense. Not for invading the middle east for corporate benefit. We've been dragged into this several times by the US in the last decades and it's always been a huge failure and has sometimes led to worse threats (ISIS for example which was much more of a threat to us than Saddam Hussein was)
A land war against China is not winnable anyway. I do think we should help Taiwan if it comes to it. But this should just come down to strategic deterrents. There's no point sending armies. By the time they get there it's too late anyway.
Our main threat right now is mainly Russia. And mainly so because they view us as enemies. But having entire tank brigades like in the cold war won't do us any good. This is not how the next war will be fought.
The US is definitely overspending for no real benefit, except lining the pockets of defense contractors(and by that, politicians pockets)
One example is that several EU armies running out of precision bombs relatively early into the Libyan intervention [1].
[1]: https://www.washingtonpost.com/world/nato-runs-short-on-some...