I'm not sure whether I agree with your "theory of operations" statement; although of course that would depend on whether we draw the "as possible" line in the same place. For me, a module should give you a good idea of how it is operating. With IO, for example, being able to tell the difference between buffered and unbuffered IO is sometimes crucial. I'm not sure you can ever get away from that kind of thing completely, or if you would ever want to (i.e., what is the opportunity cost?)
The thing about method names sounds like an orthogonality argument, which is probably quite right. You could probably make it orthogonal, but for me Perlishness doesn't require orthogonality (although it's always good). And, the documentation does tell you about < and > and when and how they work (maybe it has been changed since you looked).
I suspect I wouldn't use the overloaded operators. But, you never know. I like the shellness of them. Perhaps some of this is a case of "too cool" though. Hmm, I'm not sure.