Rock has at least 5 AA moves, but knowing when to do them depends on the range. That doesn't mean that they're not reliable though. He in no way is worse than Yuki. For starters, Yuki doesn't have many options when he's getting locked down. Sengoku requires too many frames to execute, and the window for the counter is short, unlike Shishioh's counter, or even Rock's counter, which activates instantly. The only downside to Rock's counter is when it's up against multiple hitting moves (MP's 3D) and certain moves that are long range, but have crazy hitboxes, which can make Rock whiff his flip kick. Yuki needs to charge to really be a threat.
Rock's pokes are better than Yuki's!!! You can't tell me that Yuki's 2A is better than Rock's 2A. Rock can combo with his at that!!! Rock's 2B is about even with Yuki's and that's only because Yuki can IAD afterwards, and even that he can get hit out of if telegraphed. Rock has many options from 2B. In the corner, all he needs is 2B to get a good combo in, which I've got footage of.
Rock has meter burning for AA, and his 2~8A/C. Yuki has 6A (Whiff) 3C, 623A, far B, j.C, etc. All of them can be juggled after too.
Who cares about his counter? Also, Yuki's counter is instant.
Yuki doesn't need charge at all aside from MAYBE 22D (lightning) and 22A (projectile).
Yuki's 2B is pretty godtier. Rock's 2D is seriously unsafe compared to Yuki's 2D, which can be cancel'd into a shitton of things. All of Yuki's normals but 5B / 2C / 2A / 2B can be whiffcancel'd. None of Rock's normals can do that. Yuki has a better crossup that's less spacing-specific, projectiles that actually cover space (plus they're invisible and a potential AA). He also has better punishment against things like K's AA with 214C, which combos into pretty much anything. Yuki has better mixups (left / right > high / low), and generally higher damage.
Oh, and you did write that you can corner trap relentlessly. "Rock's strategy is similar to that in "Garou: Mark of the Wolves", which is to corner trap the opponent relentlessly." He lacks the tools to corner trap at all. Whiff cancels and a good AA would be required, which he has neither of.