Omnistone will never be a preferable Keystone until...

The Keystones it cycles through are improved versions of the normal equivalents.

Literally the only reason I'd ever take Omnistone except if I felt like being a meme (like playing Aphelios and just having the maximum amount of "I'm so random lol"). I imagine most of the playerbase ignores Omnistone for the same or similar reasoning.

Having massively less control over your most important rune makes the supposed "versatility" of Omnistone a complete moot point.

It needs to have each Keystone it cycles through be a slightly better version to make it worthwile.

Situational power in exchange for reliability seems like it should've been obvious from the start personally.

Even if I'm playing a champion who can use any keystone with some success, there's no case where Omnistone is preferable because you can't control when you get any given keystone.

However, on a champion who can use any Keystone, or at least most of them, that lack of reliability might be worthwile if any Keystone you were given by Omnistone was better than the default version of the Keystone. You don't get control over which one you have, but you do get more benefit than you would otherwise as long as you're capitalizing on using your improved Keystone at any given time.

Furthermore, Omnistone will likely continue to be unappealing as long as the Inspiration tree as a whole isn't terribly appealing to most champions. Sure there's stuff in there that's kinda nice, but there's only a small handful of non-support champions who would rather have Inspiration than another tree, and those champions take it because they have a specific build or playstyle that it supports, which invalidates Omnistone, because the fact that they have a specific goal in mind means having a fluctuating Keystone is pretty inefficient.