I would say they were of mutual benefit in the past...
During the cold war America needed to be able to have its nuclear deterrent. They also needed to be able to establish early warning systems overseas as detecting a missile when it is already flying over US soil isn't much good. That means keeping nuclear weapons silos/radars etc on foreign soil.The downsides for the host country are that it automatically means they will be the first to be obliterated in any nuclear exchange. If you want to attack America, you will also take out all American bases in Italy etc. This is a massive risk so to balance it those countries get to come under Americas nuclear umbrella. And of course have military bases so the protection of boots on the ground but really, the nuclear weapons are key. In fact, one of the strategies for America during the cold war was making sure that war never came to American soil. There's no way of knowing what would actually have happened if the USSR had taken a popnat Italy. Would America have risked it's own destruction by retaliating. It doesn't really matter because people believed enough in the possibility the deterrence is enough.
But that also meant it was in America's interest to strongly dissuade even allies from developing their own nuclear programmes as they needed them under their own umbrella. Plus to be fair the less nuclear weapons the better. Also nuclear weapons are expensive so it is a saving for the smaller countries not to build them. A saving America was more than happy for those countries to make.
America might have wanted Europe to "spend more". However it was always strongly opposed to them developing their own independant nuclear deterrence**, a European army. Rather spending more meant more spending on the US defence industry. If the UK and EU (and the rest of the world) are now "dependent" on America it's a dependence they wanted and encouraged for their own strategic ends. Not the EU taking the piss. Spinning it as purely "for the defence of Western Europe" isn't entirely honest.
Trumps "golden dome" idea is basically a fantasy that they can have nuclear weapons without worrying about being attacked by enemy nuclear powers or needing allies to form a successful deterrence. It's actually quite dangerous in its own right.
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TL/DR the French have been proven right goddamit.