Yes. A stick machine lacks dynamic current control (pedal) and does not allow adjustable balance (ratio of cleaning to heating). Both are very important features for aluminum welding. And of course, you have no DC for welding steel.
You're not wrong. Using a microwave oven transformer for HF is both dangerous and not very good design. It is dangerous because there's way too much current at high voltage to be safe, and it isn't very good design because microwave oven transformers aren't designed to operate at high frequencies, so core heating becomes a very serious problem.
A simple spark gap excited LC tank circuit, as is used in most TIG welders, is much more practical. A high Q tank can produce the desired high voltage without dangerously high currents. If you do accidently load it down, the Q falls quickly, and so does the voltage, so you're much less likely to be injured.