I could see that working for very standardized courses with objective tests, like intro calc, but it'd be more problematic in higher-level courses. There isn't usually 100% consensus on how to do many things, like what constitutes a good project and what things are most important in a write-up (and the higher-level you get, the more sharp disagreements between professors get). So students and professors, fairly reasonably, bridge the gap by communicating about shared expectations. If then a third party grades it, they might be grading in a way that isn't actually consistent with what the professor asked the students to do, and with what he/she led them to believe would carry the most weight in grading.

An analogy might be going back and forth with a client on contract work, delivering a result you're pretty sure they're happy with, but then having it assessed by someone other than the client, who didn't participate in the previous discussions. It's a sort of multiple-bosses problem, which can make it harder to focus and feel confident that you know what's being asked of you.