> I'm also curious, if the cathode was grounded to the machine frame, how dangerous was it to do work on those machines?

When ground means earth, then: The chassis isn't dangerous at all. Its potential relative to other nearby things that are also connected to earth is ~0v.

When that's used as a supply rail (like for the cathode), it still works fine. It's still tied to earth.

You don't want to put any of your dinguses betwixt that and the +150v plate rail, but... I mean. :)