Why do you think the US operates NATO? We spend an unimaginable amount of money maintaining the bases, arms, forces, and other components that make up NATO. And the vast money expense is almost secondary to an even more absurd scenario where we get dragged into a scenario where potentially millions of Americans could die because of e.g. Latvia or Estonia?
There are two big reasons for this. The first is that it's completely as it seems - we want to protect the EU. But this has nothing to do with freedom, democracy, or whatever else. It's because we don't want to see the rise or expansion of another major competitor. Imagine if Germany, China, Russia, or whoever else managed to "unite" Europe, to use a euphemism. They could viably be the greatest power the world has seen in centuries.
The other is more insidious. NATO makes an EU military largely unnecessary. This is, in some ways, a tremendous benefit to the EU since it leaves them with far more wealth to do other things with, like improve their citizens' lives. But it also leaves them completely dependent upon NATO which is largely just a proxy for complete dependence upon the US. So this creates a scenario where the US is simply irreplaceable for the EU, at least not until they have their own military. And there are occasional calls for the creation of an EU military, but they mostly go nowhere, and if they did start going anywhere the US would do everything in its power to destroy them behind the scenes, and that would probably be successful.