I don't usually see "handwaving" used quite that way. It marks the argument as imprecise, yes, but not worthless. Physics lecturers who say "and I'm waving my hands a bit, but here's the basic concept, and you'll work through the algebra in the homework and see for yourselves that it comes out as you'd expect" aren't saying you shouldn't listen to them; they're saying that there are steps being left out and you shouldn't 100% trust the conclusion until you've checked all the steps.

Obviously I agree with you on "it is obvious", though.