Taliyah - Why do Champions Have Ultimates that Deal no Damage?

An ultimate skill in a champion's kit should be the most powerful, intense aspect of their kit. Activating it should feel like the defining moment of a champion's entire game, and that's why they (usually) have such long cooldowns.

Champions like Diana and Blitzcrank feel worse for me to play specifically because their ultimates are on such a short cooldown that they don't feel any different from a normal skill.

Now, there are some champions who have ultimates that make sense for why they deal no damage. Soraka's Wish, for example, fulfills her champion thematic perfectly, and that thematic is not dealing damage. Supports get a pass here, they have utility instead of damage and that utility is usually pretty defining (Wild Growth and Monsoon are equally thematic and defining).

On the other hand, there are champions who have mobility ultimates like Taliyah that suffer because of it. Specifically, Twisted Fate is the best example. Twisted Fate is an assassin who has 2 skills that deal no damage (his Stacked Deck can deal damage at the right time, but it requires you to build it up on other targets first, making Twisted Fate's Destiny a much weaker effect if you're using it out of your base, why is that fair?) Because of this, Twisted Fate has always been shackled to Lich Bane. Always. The champion doesn't have enough burst in his kit, so he has to buy an item that gives him more base damage, and he's been completely balanced around that. Why? That locks him in to a specific build, promotes the idea of assassins being completely feast or famine, and more importantly, if his kit doesn't have enough damage in it, he should gain more damage, he shouldn't be chained to an item that makes up for his imbalance.

Tahm Kench is another example. Tahm Kench gains damage on all his abilities and auto attacks (which is not thematic, not cool or intense, and pretty uninteractive as a whole for your opponent) in exchange for a team-transporting effect that no one uses. Devour could be Tahm's ult instead, very very easily. It's a suppression effect, which is huge, it saves your allies which is his highest point in the game, and it would allow him to have a real passive, a real cooldown on his suppression/ally saving effect to make it more valuable and less frustrating, and a W that's more appropriate for the laning phase.

And now Taliyah. Cool, she gains an instant speed mobility tool. She already has one on her passive, but this one is faster. And in exchange...either her kit is going to have damage forced into it or her bases aren't going to be enough and she will be shackled to Luden's Echo or Spellblade.

Can someone please explain to me why these effects have to be in the ultimate slot? Aurelion Sol's map mobility is totally fine, and it promotes him roaming even though in combat he's actually pretty immobile. It has a real cooldown because of the stacks, but it also doesn't detract from his ultimate which has actual damage so he isn't forced into any cheesy builds.

Or you could just give the mobility damage, like Pantheon or Shyvana.