Matt, I understand that you are writing primarily to your graduate students, but I also have to object to your first two points in general. I am a counterexample, as I took 12+ unnecessary math classes (getting A's in them) on my way to a successful PhD in theoretical computer science/crypto. I've found that my background in math has given me some tools and perspective that improve my research (I recognize when we are constructing a finite field in a round-about way, or when the abstraction we really want is a group action, or when Borel-Cantelli is really needed to make an argument rigorous, etc etc). I wouldn't have obtained these tools without a huge investment in time at some point.

Actually, I still find myself reading and learning unnecessary math papers most evenings as a hobby. I think it makes a huge difference.

Perhaps this is unique to mathematics, where theorem proving skills are portable. I certainly wouldn't use my situation to argue that PL grad students need to study French. But maybe the PL students should take an extra distributed systems course - and TA while they do it!