OK, but now you're arguing that Yale students shouldn't be exposed to free expression because they're incapable of handling its consequences. I think that's silly, but fine: it's a real argument. But let's stop pretending this kind of paternalism is consistent with even a modest notion of free expression, because it's very clearly not. It says "you can only say things we approve of, because we know best." Being right about knowing best doesn't make it not a limitation on free expression. Free expression as a principle necessarily doesn't hinge on whether you think the individual expressions are right. That's, like, the whole point of it. [1]
You're also arguing that 1-5 rating systems are silly and Yale shouldn't bother collecting them, but that has nothing to do with the YBB+ website or how students will interpret it. For example, wouldn't those perverse incentives you mention be in place already, given that providing feedback to professors was the whole point? Ratings don't magically transform from useful evaluation tools to misguided oversimplifications just because students have convenient access to them. Either they carry useful information or they don't.
[1] I'm not taking a free expression absolutist position here. (I'm tempted to, but it's totally unnecessary for this discussion.) The point is that to the degree to which you make rules about what kind of thing people can express is, well, trivially the degree to which you limit free expression. And limiting the ability of students to transmit truthful data about the courses they're taking is a very strong limitation, and it would be hard to formulate a consistent, principled policy that permits this kind of restriction and doesn't just say, "you can't say things we don't like".