Mm... I would say that a typical dragon does have an extremely large ego, enough that it can be a disadvantage. However, it isn't stupid. It's a cunning, resourceful fighter and uses its abilities to the fullest. It certainly doesn't land and go into melee just for the heck of it.Dragons with overlarge egos don't live to be old. So we don't play them with an ego that makes them want to enter melee and risk their hide. We play them with an ego more like an evil genius where they use their physical superiority in a very intelligent way that disallows the party from bringing their full might upon the dragon.
Tactically, the dragon's weak point is that it hates to admit defeat, even temporarily. If it discovers that its opponents have unexpected resources, it's likely to stay in the fight rather than pull back and reassess. Only when it's clearly losing will it try to retreat, and by then it may be too late. Likewise, if its opponents withdraw to a position where the dragon can't easily get at them, it may try to force its way in or it may try to wait the opponents out, but the one thing it won't do is concede a draw and fly away. The longer its victory is denied, the more irritated it gets. When presented with a way to end the fight quickly, it's apt to take it without more than a cursory check to see if it's a trap.