Bringing certain champions out of their intended roles tends to bring a lot of unforeseen and often toxic consequences.
Your example with Alistar vs Jayce gets broken down when you realize that a) Most of Jayce's burst damage (gate blast) can be dodged, and gives Jayce a moment of weakness when he doesn't have one of his strongest damage abilities and he just used up the closest thing he has to an escape, whereas b) Alistar's W harass can't be avoided. Especially if Alistar gets a Sheen or its upgrades, he can be doing a lot of damage that many top laners literally can't respond to, AND because Alistar's W knocks the enemy far back, it doesn't put Alistar in any significant risk using it like Jayce's combo. There's also the fact of the matter that Jayce is a damage carry and is supposed to be doing a lot of damage, whereas Alistar is supposed to be a tank and not doing as much damage, so the fact that Alistar's harass combo not only isn't counter able, but it also hurts a significant bit is beyond problematic. Jayce also has only 500 AA range in cannon form, which is usually much less than many Top Laner's hard engage. Especially for the more bursty top laners, a well timed engage while Jayce gets too close to harass can easily lead to a very injured Jayce.
Now, Warwick vs Alistar. Yes, Warwick has good ganks, every 90 seconds after Level 6.
The moment Alistar is level 2, Alistar can potentially gank nonstop and each and every time his ganks are terrifying for enemy laners.
AD Nidalee was nerfed because she carried all three aspects of what can and should make a champion strong. Her AD ratios were high enough to do significant damage with only a few items, this freed up space for her to build tanky/bruiser and make her hard to kill, and the slow based items gave Nidalee CC, even if soft. This iteration of Nidalee carries all three strengths of Champion design without a significant drawback for it (for example, Raid bosses like Nasus or Trundle have all three of these aspects, but I'm 90% sure everyone knows why Nasus and Trundle aren't problematic if you don't just leave them to free-farm for half an hour). This is actually part of the argument against Alistar in your Jayce vs Alistar example. Jayce is only able to carry, at most, 2 aspects of champion strength to a useful degree. Jayce automatically carries utility thanks to his Cannon form, Gate, and Knock Back, and due to how his scaling works, Jayce must choose between getting very tanky or building for damage. Alistar on the other hand already has utility in his Knock Up, Knock Back, and Heal. Furthermore, Alistar can build full damage and still be tanky as hell thanks to his Ultimate, thus bringing us to see Alistar carrying all three elements.
This same argument follows for Yasuo, a melee carry (which means lots of damage but not much tankiness) who focuses on Utility. 2 Aspects.
The opposite argument follows for Kayle, who's ultimate and Heals ultimately gave her Utility and (even if technical) tankiness even if she was building full damage.
Kha'Zix was nerfed to the ground for building tanky and still doing too much damage. With the mobility of his resetting jump and his Isolation damage being quite the tool back then, Kha'Zix is yet another champion who carried all three aspects to a strong degree.
Yi has no tankiness if we consider his meditate as utility, and extremely limited utility if we consider his W as tankiness.
Tryndamere has very little short term utility (if we treat his ultimate as tankiness)
Rengar is yet another tanky champion with burst damage and utility.
Anyone who is overpowered due to how their kits function on the technical level is getting nerfed.
