When fighting on the ground you can always get close. To allow a melee character to fight on a flying creature the game would have to be biased so that no creature could fly faster than you could (so nothing could hit and run repeatedly) and there were no effective ranged attacks.

The same goes for our plain old ground to ground attacks, why would it be different for air to air or air to ground. You can get close because it is biased, else some fast running ranged attack user could always just hit, run abit hit again, run abit,... with you just running behind it staying out of reach. I don't see why this is suddenly different in air to air.

In most traditional RPGs flying creatures were limited for balancing reasons, to allow for melee only characters. Adding the ability to fly (especially with a creature having a natural ranged weapon in a lot of mythology) and keeping all the same limitations and restrictions seems like a waste of potential. Why fly if you are fighting the exact same types of monsters with the same behaviour as you were on the ground?

Thinking about this some more, melee only dragons wouldn't necessarily force ranged weapons to be restricted as much as they traditionally have. Any flying creatures with ranged attacks would have to be in areas inaccessible to the character in human form, though, unless there was enough cover to protect them.
Effective ranged attacks would make melee dragons have to attack fast (dive from above, grab something, kill it and break away before hitting the ground), use surprise (sun/clouds as cover, or some kind of stealth magic) or brute force (frontal attack trying to avoid as much as possible, using a magical shield or possibly even picking something up and carrying it to protect against attacks from below).

There would still have to be limits to the number of creatures in a group with ranged attacks. In some cases perhaps attacking the leader first would cause the rest to scatter, giving you time to go after some of them before they could regroup.

Speaking of picking things up as a dragon, it would be cool to be able to grab stuff (trees, boulders, cows...) to carry somewhere and drop on an opponent. Of course the environment would already have to be at least partly movable and destructible for anything like this to be implemented.