It's pretty telling to see Germany refusing to buy F-35 or Hungary buying ones in order to piss off Sweden.
And if you're going to be training pilots... Shouldn't you do it on the exact config of F-35 that Denmark's buying? Which means a Danish F-35, which means leaving it in the US.
That aside, it's more or less common knowledge these days that the planes have not been delivered for all these years due to the production problems they are still having.
Esquire just did a piece just month mentioning that the plane starts to fall apart if it's flown too fast and the computer fails to detect if the plane is flying to fast about half the time.
This aircraft program still has a ways to go.
We don't know what the "training in the US" requirement looks like, though. I wouldn't be surprised if it was just "you need to use Danish planes to train" + "we only have training facilities in the US, and if you want to bring your own that'll cost money". It has nothing to do with "Denmark can't make its own decisions", because as far as I'm aware that hasn't been alleged anywhere.
Having a military costs money. Living up to treaty obligations like NATO costs money. Trying to have a military on the cheap just ends up with dead troops/pilots/sailors.
India also has lots of land.
For the F-35, other countries were asked to pay into the R&D budget, with the promise that large contributors could obtain exclusive manufacturing rights to certain components. I've seen a lot of grumbling about this, with people claiming it traded cost savings for a military risk that the planes will be useless (or at least lack spares) if things go wrong for those suppliers.
This is sort of true, but the missing insight is that the dependency is also a goal. It's not going to allay fears that F-35s are calling home with telemetry or have compromised software, but it does help create reciprocal interests in the same way as inviting in a foreign military base.
I think it extends the metaphor to NATO very well actually. A mutual-defense alliance gradually turned into a political and economic alliance, and now it's not clear how well the original proposition can be trusted. RAND, at least, thinks Estonia and Latvia can't be actively defended and couldn't be retaken without bombing campaigns in Russian territory. So suddenly, the strength (or at least universality) of that agreement becomes an open question.
All of which means that it's more or less impossible to buy a weapon from a foreign power without opening yourself up wide to that power. You have to let their military advisors onto your bases, to train your troops on the doctrines that go with the weapon. You have to let their logistical specialists into your inventory systems, so they can hook you into the pipelines through which the spare parts and ammo flow. Any of these people could be using their access to snoop on you or worse, but there's not much you can do about that because without them all you've bought is a $100 million paperweight.
If you're the buyer, yes, that absolutely sucks. But, unless you're willing to spend vast amounts of money you don't have to build up your own domestic military-industrial complex, you don't have a lot of alternatives. You either buy into one of the existing ecosystems (American, Russian, European or Chinese), or get curb-stomped by a neighbor who did. Once you're bought into one of those ecosystems you're effectively at the mercy of the state that operates it, of course, but hey, you do what you've gotta do. As the saying goes, the strong do what they will, and the weak suffer what they must.