I'm sorry for shitting on your job, but it seems like the solution is to bring back the buttons we had in the 80s and 90s and drop all the software garbage? I don't want a UI, I want an On button.
It's fine, I take every opportunity I can to shit on my own job lol.
Ironically what you're looking for can be found in the lowest end, and the highest end products. Low end means low features, so you can get away with just a knob and maybe a few LEDs. Look at Hotpoint (GE's low end brand) or a low end LG washer [0].
High end usually forgoes a flashy UI as well since it's about the style and being a centerpiece.
The mid end is where it's weird because features justify the extra cost. In order to make those available you need to have an LCD screen and more buttons.
In all these categories you'll run into software though. It's cheaper than a electro-mechanical solution. We only fall back to the old ways when required for safety/compliance.
You will probably find the ones you like with simple interfaces and a few physical buttons for an additional price. Simple things are now premium.