Riding something, anything, into battle makes you a priority target for the enemy, whether your mount is a horse, a dragon or a tank. A mount of any kind signifies status, special abilities and/or a particular role, which gives the enemy every reson to want to neutralise you. Having the enemy's attention is usually not very healthy.
If not in a battlefield setting, I probably wouldn't bother with a mount anyway. I mean, a dragon or a tank would be cool and all, but it's just waaaay too much fuss. A dragon's got to eat, it needs somewhere to sleep, probably in shackles and under guard, and it's probably not too popular with the neighbours at any rate. A tank requires a ridicilous amount of maintenance, spare parts and tonnes and tonnes of fuel, not to mention it's a pathetically inefficient and uncomfortable ride. I could maybe do with a car. Maybe. Or a bicycle.