A full-time code reviewer will quickly lose touch with all practical matters and steer the codebase into some unmaintainable mess.
This is not the first time somebody had that idea.
I think it's amenable if you make code review a primary responsibility, but not the only responsibility. I think this is a big thing at staff+ levels, doing more than your share of code review (and other high level concerns, of course).
Linus Torvalds is effectively a full-time code reviewer, and so are most of his "lieutenants". It's not a new idea, as you say, but it works very well.
I've often thought this could work if the code reviewer was full-time, but rotated regularly. Just like a lot of jobs do with on-call weeks, or weeks spent as release manager - like if you have 10 engineers, and once every ten weeks it's your turn to be on call.
That would definitely solve the "code reviewer loses touch with reality" issue.
Whether it would be a net reduction in disruption, I don't know.