In theory, a fixed 15,16,16,18° fixed sharpener is fine, my EDC from Olamic is set at 18 and they don't recommend anything steeper. Their steel is great as far as heat treatment etc. That's not a chef's knife of course, but after 3 years of pocket time I have never had the desire to re-grind it.
If the Tumbler can remain consistent, I don't see why you couldn't figure out how to sharpen the whole length. Same as any other sharpener, you practice with what you have.
I use TSPROF, and have a rotary grinder with wheels up to paper, but you can't easily travel with either. If you can maintain the consistent angle, the steel doesn't care the same way a circle doesn't care if you use a grammar school protractor vs. any other tool.
I'm interested in any feedback from someone who has actually used one too, same as OP. Most people suffer from confirmation bias after spending hundreds or a thousand on the best tools, that's just human nature. But it would be nice to have something portable that doesn't destroy blades like a pull sharpener!