Mount Farm, but in Ultimates please.

[Nezerius]

The cool, and unique, weapon visual effects should be motivation enough. It's exclusive content for the like 1% of the 1% who isn't satisfied with savage raiding and wants something harder; there's no particular need to focus on giving it an increasing number of exclusive rewards non-ultimate raiders can't get.

While Ultimate is definitely hard to clear, "1% of the 1%" is exaggerating a bit too much.

Using ffxivcollect (a website used to show collections/achievements in XIV), it shows that 9.3% have cleared Ultima Weapon Ultimate at least once. In comparison, 21% have completed Eden's Promise (Savage) at least once.
Now, the disclaimer here is that the website obviously doesn't show the data from every single character ever created. However, the sample data should be large enough to create a rough estimate on how many players have cleared an ultimate compared to how many have cleared the current Savage tier. That's also excluding the amount of players who are still attempting to get an ultimate clear.

OP's suggestion doesn't sound like it'd take a significant amount of resources either, since it'd be reusing models from the fights itself. And while clearing it 99 times sounds like an absolutely insane grind, it's not like XIV doesn't already have a bunch of those anyway.

The reason there are no Ultimate mounts is because SE doesn't expect most players to do Ultimate. In their words, you are more likely to watch it on a twitch stream than do the content yourself. For this reason the most it will give is a glamour, a title and an extra materia slot.

The content they expect players to actually clear is Savage so this drops item level increases and mounts.

How would you explain the existence of Feast mounts? Only the top 100 players of a datacenter get these, so SE doesn't really have an issue with adding mounts as exclusive rewards. Not to mention the Pteranodon mount, which is currently the rarest non-Feast mount.