BTW, the skip-level concept is something I gleaned from the Manager Tools podcast. I highly recommend it for anyone interested in learning how to manage better (or even, just, understand organizational behavior).
Speaking as a manager you'd be surprised (actually scrub that, you wouldn't) how often when I raise concerns the team has the instruction comes back "screw what the team thinks or wants, just do X" (where X flies in the face of what the team want and best practice but supports what the screaming customer and short term revenue demands).
Organisations that genuinely care about the staff I don't think would change much, those who don't won't ever do it so it's kind of moot.
Probably microscopic shitstorms, not large ones because only a minority is affected. But in the long run it would probably change everything in organizations with management problems. I think hiring policies would also change a lot.
That HR doesn't understand what you are doing is a bad excuse, depending on the job you might be the only person knowing exactly what you are doing. Anyway, I feel like the manager doing the review is absolutely unfair - at least not in a sufficiently large organization.
>it would cause too much gaming the system in either retaliatory
This is already the case. When your manager does the review, your review is limited by the manager.
As a consultant I worked for several large IT organizations, and I got to see a lot of very toxic people. Some were really high up, some middle managers. They were assholes with everybody but I bet they were very nice to their own bosses, and worked very hard at masking their incompetence. Those people can really screw the organizational culture.