The big reason militaries around the world didn't go after the dragons when they first appeared was, most likely, due to all the WTF feelings everyone was experiencing. Not to mention all the chaos that was happening simultaneously. No one wanted to start something that could easily escalate into a strategic nuclear exchange (hint: NO ONE wins one of those).
The big 'D' was quick to assert to everyone that "Hey, we're all just folks around here" to everyone. To "humanize" the dragons (so to speak) and provide everyone with some context with what was happening. This made a lot of friends in the mundane world, friends which the dragons needed. By the time all the weirdness got sorted out, dragons were a part of life (unusual, to be sure, but part of the world we live in). The dragons, of course, took advantage of this time to settle in and figure out the new world they awoke into.
So now, 60 or so years later, everyone is used to dragons being around. And the wizwurms now have the resources and allies they need to be serious trouble if someone should choose to try to off one. As said earlier, the status is now quo.