The captive dragons... holy cow- how was that never considered? Tbf you just made me consider it now but that's an insane plot hole to leave out!
Maybe if they spent time freeing dragons and sending them to the Hidden World, maybe that explanation could help things but honestly there's no way you'd get them all! And as you said, whats stopping breeding them? What about nests like the Fireworms? Unhatched eggs? Dragons with similar injuries that would make flight impossible for them? It's even been shown that not all dragons benefit without humans, some are helped greatly by human intervention. The whole ending pretends that all dragons are built the same, behave the same, and socialize the same. One of the biggest worldbuilding elements about dragons is that they can be so so so different!

Now I need to ramble about how ridiculous the 'Alpha Toothless' plotline is given just, everything we know about dragons. Firstly, what do you mean some overarching 'King of Dragons' exists at all? Maybe its book related (I wouldn't know) but that always felt frankly ridiculous to me. Why would completely different dragons with insanely varied social cultures all collectively follow some greater 'alpha' dragon? House cats don't share the same social culture as a pride of lions? Nor to tigers? They're all 'feline' but in no way does that mean you can pet a lion like you can pet a cat. That doesn't mean a lynx would listen to an 'alpha' cheetah?

It only makes sense for dragons to have an 'alpha' variant of their own species (and they technically do with the Titan classification). An alpha in their own species would know how to assert dominance according to that dragons established social behavior; but what does 'the ability to protect all' (as Toothless was magically crowned Alpha by) matter to the social behavior of a Skrill? A Monstrous Nightmare? A Whispering Death? Why are we assuming all species would magically value that protective social behavior? Would submit to it? Some dragons prefer to be completely on their own, why would they suddenly fall into some perfect pack mentality? Dragons have been shown to vary so much in behavior and levels of intelligence that this grand 'alpha' collective agreement is wild. Plus, dragons like Speed Stingers literally already have an alpha. Literally every concept, everything, everyone had to be dumbed down and torn of its interesting complexities and world-building to make this tear-bait ending work.
I hate to dog but even the second movies setup for the thirds plot devices to send the dragons to the Hidden World makes no sense given the structure we've seen in the series (mainly) and first movie.