I'd say Tryndamere and Xin Zhao are both examples of light fighters, rather than divers (they tend to build primarily for damage, rather than durability, and tend to have much more difficulty reaching the back line than, say, Irelia or Vi), but pedantry aside, I completely agree that this is a good time to have some preliminary discussion on divers, especially since Riot just released one with Camille, and made a dev blog about how she was intended to be a good model for the subclass.
While I agree that divers have issues of shallow gameplay and old, often rushed kits (a huge number of divers were made in Seasons 1-2, when Riot was pumping out a new champion every few weeks purely to generate more content), I think the biggest issue with the subclass right now is that it's generally overloaded, and has no definite weakness as a whole. Even light fighters, who are notorious for their overloaded kits, tend to be squishy, but divers are tanky DPS champions who also happen to have a ton of mobility, plus often some crowd control and burst. We even have some divers whose burst approaches that of assassins, with Lee Sin and Jarvan as some of the biggest examples (Riot even did a post on AD assassin Jarvan mid), so really, the only in-game feature they tend to not commonly have is ranged attacks (and even then, Lee and Jarvan both have poke). I feel the Diver Update would be a good time to strip divers of excess strengths, e.g. burst damage, but should also be the opportunity to give them a consistent weakness: as mentioned in the OP, gating all of their mobility, crowd control and utility behind heavy cooldowns, which they'd have to use sparingly over the course of a fight, would allow divers to keep diverse kits, as well as deal a baseline amount of DPS, without just filling in as off-tanks and pseudo-assassins in the process.
are in much more need of changes to make them more thematic than tanks like
