Not completely homogenized, there’s:
- submarines, (not sure they all have the same speed)
- runners, (one is slower and useable at level 1)
- runner+fliers (2 can pick plants)
Independent of that:
- Some have a passenger seat or two, some seats have vendors in them.
- Some are restricted to certain factions, classes, specs, professions, instances.
- Some fit through some doors, some don’t, depending on the race riding it.
And that’s it for mount diversity. The rest is purely cosmetic and variations on how their obtained.
Once obtained… That’s it as far as customization goes. Which is too bad.
Instead of player housing, I’d rather have a system that let us customize our personal mount… Visually and functionally. Style, Color, saddle (s), vendors, size, speed, domain (air, land or sea), armor. Let our professions and class unlock extra styling options and functions… And abilities.
Build in trade offs, like: too much “stuff” makes it slower, or slightly increases mount time. It makes it sink in water. 
Basically just add whole slew of mount crafting and transmog abilities … With options we can collect, hidden all over Azeroth.
And not just for our personal “favorite” mount… But for a custom “guild mount” as well.
Heck… do the whole artifact weapon thing again, focused on mounts… And let us keep using them afterwards!