> Even more so as American armed forces and weapons (and our tax dollars and political system) are what protect all of you from annihilation.

It's a lot more complex than that and a lot less cartoonish. The US armed forces protect the way the world is structured, which is obviously dominated by the US. This state of affairs has been erected over the second half of the 20th century primarily to further US interests. It's relatively unique in that it has come about with incredibly little bloodshed, though there are some precedents (not at this scale, obviously). This state of affairs has worked really well for the US as a nation state and economy, and it has had a ton of positive collateral effects for many others as well, but of course nothing at this level is ever motivated by goodwill. Protecting the current world order is done out of self-interest.

The European powers have arranged themselves with and taken advantage of this reality pretty well. Yet no one (that matters) is under the delusion that any support or protection on the part of the US happens for any other reason than to further US interests and wouldn't happen if those interests weren't aligned that way. The US are a "force for good" if and only if your interests are aligned closely with theirs; find yourself in the way of US influence or economic interests, and things can get very evil. There are numerous examples for this in relatively recent history (the most recent one is probably the Julian Assange extradition ruling).

If you look closely, you'll also notice precisely how the big EU players accomodate for that reality. Obviously the US wouldn't tolerate a European rival and it's certainly much safer to keep those interests aligned, given the scale of US dominance. It would also be a lot harder, geographically, to build a powerhouse like the US on European soil, and an impossibility from a political point of view. So there's no upside to aim for overwhelming force projection capabilities on a global scale; just huge risks and downsides and crippling cost.

Yet France and the UK have nuclear arms and fairly effective militaries that are way, way smaller that the US one, hence not a true rival even on European soil, but cover the important strategic bases; namely a solid capability for limited but effective projection of force abroad and a nuclear retaliation capability. Germany, due to its geographic location, cannot have either, as it must not seem threatening to its neighbours if Europe is to have any kind of stability at all. Poland couldn't possibly chain itself to a Germany poised to pounce at them whenever a hardliner government comes to power and France would have similar reservations, they're highly exposed to attack from the northeast as well. Germany's weakness is why the current state of affairs can exist, with a EU security policy that revolves around the tightly-coupled binary of France with its strong national defense stance and Germany with is baffling lack of strength.

Yet it's widely acknowledged that Germany is a latent nuclear power and could build nuclear weapons and means of delivery very quickly with resources present on its soil if it decided to do so. Even its military, joke of a force that it currently is, is fundamentally built to scale into a very effective modern army relatively quickly (as in a couple of years), they have a lot of expertise, just not a lot of decent hardware or effective organisation. It's likely that they will do some scaling now, depending on how the Ukraine conflict develops further. If they do, it's going to be interesting to see whether that actually works the way it's intended to.

But as long as the US are both capable of and forced to intervene in any major assault in or on Europe, or suffer a huge loss of influence and severe long-term consequences to their economy, being strategically cheap in that department is a pretty solid gamble that brings a bunch of benefits the US cannot enjoy, like being able to treat with Russia and China with a lot less reservations and being perceived as a lot less of a threat (especially in case of Germany). Whether getting cozy with China is a good thing in itself is of course very much open to debate, but the EU powers simply don't have the kinds of interests in the South China Sea that the US have there, that does open up options.

> the same issues plague both sides

Some of the issues are common; most are not, or only superficially so, with what will probably be very different trajectories (by what might well be a large margin). Europe is a very complex place, too, a very old, very cramped constant battlefield (literally; up until recently, there was literally always someone at war there), it is geographically linked to half the world, deeply divided, has few natural resources (left), is perpetually struggling to not lapse right back into constant warfare (that's what the EU is for), has no common language, no common set of ideas or values, no strong common identity and it's chock full of ancient grievances and conflicts papered over very thinly. That gives rise to tensions the US don't share (and vice versa – the unique situation in the US poses challenges that Europe doesn't have).