We can only imagine what a world would be like if there were real dragons, what I reject is this idea that no nation anywhere would arm and train their citizens. England has a ton of coastline and there was a long history of being raided, it makes sense that they would want most people to have an ability to defend themselves.
Just to be clear, that wasn't at all the purpose
of training people in longbows and maintaining that training.
At the time, most of Britain hadn't really been raided for hundreds of years (the South West is a slightly different story but longbowmen didn't tend to come from there). Further most of them were fairly deep inland.
The purpose of the edicts forcing longbow training was to ensure that a fairly difficult-to-maintain resource (at other countries did not possess in the same way) was maintained, which is to say, a supply of well-trained longbowmen. Not just the small standing army, but people who could be drawn upon when it was time to go shoot from Frenchmen. And that army was primarily used offensively, or at least outside the borders of the British isles.
You seem to be thinking of it like American "Minutemen" or something or Wood Elves sentries or something, who are there primarily to defend against what is perceived as a regular threat. That's the wrong way to look at it. This is the government forcing people to train so they'll be ready to fight in their wars, not to defend coastal settlements from Vikings who hadn't raided them for 200+ years.
Thus it doesn't really make sense re: dragons.
Re: dragons the government is going to make a sanguine decision - do they lose more people/houses/livestock/crops trying to fight off dragons, or just fleeing from dragons. If you can kill dragons with a few dozen or hundred men with bows, dragons will be hunted to extinction within generations, at least in populated areas. And there will be armies and expeditions going after the remaining ones, even in frontier areas. I mean, jeez, just look at how tiny or perceived threats are reacted to throughout history.
There isn't going to be any passive-ass "I guess we should arm everyone with a longbow in case a dragon comes". They'll hunt them to the ends of the earth.
If you can't
kill a dragon with a bunch of guys with longbows, then suddenly we get a more D&D-like situation.