No one is exaggerating anything. Ryze's root is so powerful precisely because it is reliable; he can apply his damage without worrying about every coming close to missing. And because his primary damaging ability is also the only skillshot in the deck, having instant CC to make that burst unmissable is ridiculous. Other mages may have better CC, but none of it is targeted (outside of Annie, who's a different problem entirely). Not to mention most other mages have damaging ultimate abilities, whereas Ryze has to make up for that by having competent, more consistent damage combos through basic abilities only.
I also don't understand why you decide to use Ahri, a champion who spits in the face of immobility, as your example of a lane opponent. Her wave clear is abysmal, you don't even need to trade with her unless its reactive trading. Just shove the wave and watch her struggle to keep up or roam because of your stronger wave clear. Careful use of your E and Q can even let you trade with her through the minions in proxy; she won't be allowed near her wave frequently because you can damage her by virtue of minions, not based on whether or not you can root her.
Any Ahri with ult would likely hold her Charm until you root her anyway, simply to screw over your entire combo. The problem for Ryze here is he will get charmed when he roots, which prevents him from applying his damage. Having a bad match-up isn't a bad thing for a champion, it's expected.
And his only nerfs are to the movement speed and shield he gets from consuming 2 Runes. His damage is literally untouched.
If you want to keep his root instant target so much, that's fine.