I think, as you mentioned, this wasn't a problem with mounts but rather how they were handled. Being able to whistle one into existence whenever made them essentially a buff every character had. If instead mounts were iterated from the UO system, where they were part of the world, and could die or would need upkeep and say, wouldn't go into dungeons so they'd need stables and all sorts of other overhead--they could actually be a mechanic that would be used in a more discriminate fashion, like say only for long range travel.
I feel like there are a million ways to iterate on the concept of mounts that were never explored because they essentially became a "buff with graphics". Fun ways, too. Even ways that promote social interaction (Like having to buy your mount from a druid or ranger---because they have the ability to find them, and train them, from the wild). Lots of cool areas there that were never explored because it became popular to view mounts as a specific type of mechanic that only offered benefits, rather than pros and cons.