I know what you're thinking, but hear me out.
These rare drop mounts, things like Spawn of Horridon, Blazing Drake, Razzashi Raptor - stuff with a 1-3% drop chance from raids & dungeons are so rare that realistically you will probably never be able to get them... at least not the raid drop mounts. If you're lucky you might see one drop during progression but the chances are that even if you come back at higher levels every week to farm it you'll still never get one.
Now you might say that's good, it makes them 'special' for the few that do have them... but I question the validity of that statement. I question the point of something so rare that it seemingly doesn't exist, and I wonder how it would be if the drop chance was even 5%, instead of 1-3%?
Some people will say that if the chance was increased slightly that suddenly everyone will have one, Stormwind and Orgrimmar would be full of Clutches of Ji'kun.... well that simply would not happen - even if everyone did own one not everyone would use it, and that is a fact often overlooked. But the point remains that this is an over-exaggeration, and my intent is definitely not to make them so common, but to simply allow a worthwhile number of people to realistically obtain them.
The mounts will still be rare, but not extremely rare as they are now. And regardless of how many people might actually own them, you still wouldn't see an excessive amount of them due to players' personal choice. In fact, the frequency of which you see people riding rare mounts is unlikely to noticeably change.