I don't think I've read many CYOAs where third person did work. Or first person for that matter. If I did, it must have been good, becaus things like PoV and dialogue tags are something that should melt away in proper immersive writing. I'm sure it could work, but ultimately if you've managed to reach the nebulous point where your writing is good enough to pull it off, it tends to blend into the background noise as most narrative does, and doesn't have that much more than a subconscious effect.
The thing that takes me out of first person is that it feels like someone else is telling me something they did, so when it comes time for a choice, a lot of work has to be done to pull that off without a hitch, because under most normal circumstances, a person telling you that story would be well aware of what happens in it. From a third person perspective, things do work a little better than first, but something feels strange about making decisions for other people, though I suppose that's just years of experience with the other voice messing with me. I could get used to other story PoVs.
But I feel like using "you" pronouns is nothing restrictive at all. If you truly made a fleshed out character, that would be readily apparent. They'll likely have their own name, they'll say things without your input, and also perform actions of their own accord, their choices will be limitted to solutions that they would come up with. It's readily apparent to anyone who isn't stupid that Suzy or numerous other Endmaster protagonists aren't supposed to be the reader, and seeing a narrative directly from the eyes of a character does not necessarily mean you're supposed to be them.
Consider most First-person games, which are more or less the equivalent of visual media addressing the character as "You" and centering what happens around "You" specifically. Sure, some protagonists aren't fleshed out and are made to be blank slates, but the Postal Dude is definitely his own person with his own nueroses and not supposed to be the player at all. You're just faced with the choices he would've had, and allowed to choose from the options he would've picked.
Of course the person "controlling" the character will imprint some part of themselves on that character, but that's true of any character with any degree of separation from the audience. Characters are supposed to be related to in some way, that's why we don't write about furniture. If seeing the world directly through someone's eyes and only having their sensory input to the story meant that they had to be blank slates and the reader themselves had to provide all the input, then we wouldn't have characters like Duke Nukem, Master Chief, the TF2 Mercernaries, and so on and whatnot. But those are only Action Game protagonists, an entirely different medium just to easily illustrate the point because my brain is small and tree-shaped and thinks only in images with long monologues.
In storygames, you have even less control of what the player character is doing, so the actions they perform independently of the audience should shine the most. That's a Storygame's strength. There are plenty of actual storygames on this site that prove your thesis wrong to begin with. I daresay most featured games on the site are not possessed of blank slate protagonists, but they are second-person.