I kind of agree with this even in a broader sense. Part of what has made it so hard to balance the meta, and has restricted styles and champion picks so much is the necessity for champs to be generalists.
Once you release a few champs who have good mobility, good damage, decent laning phase, at least mediocre wave clear. Why would you play anything else?
In my opinion that game would be much more interesting if champs, as you said, were slightly more one dimensional. For every strength they have, they should have a glaring weakness elsewhere in their kit in direct proportion. Annie has low mobility and mediocre wave clear, and unreliable CC. In that context her being able 100-0 someone in one combo makes sense. If damage is literally the only good thing about her, then her damage should be insane.
That same mentality should be carried over into most champions. I'm not saying every champs should be one dimensional, but I absolutely think one dimensional champs should have that one dimension strengthened to a point where they are viable at pro play. And I think the game could benefit from having a couple more champs with kits like that. And for a certainty all champs should be with that mindset: IF YOU ADD STRENGTH IN ONE AREA YOU HAVE TO REMOVE IT FROM ANOTHER AREA IN DIRECT PROPORTION.
For me, a champ like Yassuo have far too high of a ceiling. Certainly, he is heavily gated by mechanical skill and player confidence. But, I think his potential is far too high when you consider: he's highly mobile, he's got good burst damage, he's got good sustained damage, he's got a very smooth power curve throughout the game with no major troughs and scales insanely, he's got one of the strongest non-ult enablers/defensive tools in his W, and his shield allows him to be tankier than assassins and in fights where he is allowed to dps he becomes nearly as tanky as a juggernaut due to regen on his shield.
What Riot should do when designing a champ, is provide categories and designated number scales. Every champion should have an overall power level of say 50. Then Riot creates categories like burst damage, sustain damage, offensive utility, defensive utility, mobility, tankiness, single target damage, aoe damage, attack range, vision/map control. Then each of those cats get's ranked 1-5. If the number you come up with is higher than 50, the champ needs a nerf. If it is lower than 50, it needs a buff.
A universal approach like that will balance the game and allow both champion AND strategy diversity to be in the game. Which is something that seems to be missing.