I think that the best microwave UI is just two analog knobs. One for power level (although it would be nice to get rid of this as well, but some packaged foods ask to be cooked at 50% power for part of the time), and one for cooking time which also starts the cooking if the door is closed. Turn the nob to whatever time you want and it starts cooking. If you want to stop cooking before time is up, you can either turn it back to 0 or just open the door.
My parents still use a microwave they bought before I was born (I'm 28), and it does exactly this, except without the power dial. It's one analog dial for time -- turn it to start, turn it back to zero to stop. I miss having it around.
The best microwave UI I've used has several functions above the number pad, all of them completely optional. Typing a time on the number pad and pausing made the microwave start -- to rephrase, if you press 4 5 and didn't press anything for 3 seconds, the microwave would begin and operate for 45 seconds. Pressing 1 3 0 and walking away would run it for 1 minute 30 seconds. When it was done it beeped 3 times, then once every 10 minutes, until you open the door or press a button. At the bottom was a Power button which you could press to change the power level at any time, and a Start / +30 sec button which would add 30 seconds to the amount of time on the timer. And if the clock wasn't set, it would just display 00:00 solidly, not blinking.
Maybe this is a mis-remembered mix of the best UI elements from several microwaves, but to me it's ideal.
My grandparents set their house on fire by microwaving a potato for 50 minutes instead of 5 minutes. It's going to be really hard for any UI to compensate for that kind of disadvantage, where a subtle difference like pressing a digit an extra time can set your house on fire. The +30sec button is a reasonable button-oriented approach, but dials are a lot easier to use.
I'm also not a big fan of your "walk away while the microwave is off and it turns on after three seconds" model.
I would like a microwave that has exactly this kind of two knob UI, but implemented by solid state electronics. Across last five years or so the root cause of almost all broken appliances in my home was some kind of mechanical sequencer that somehow failed and cannot be reasonably fixed and finding it as an spare part somewhere is practically impossible.
With digital you can heat for a specific time and power, so it's replicable. This is great when, say, heating milk for a baby or water for Aeropress. There's a big difference between 30 seconds and 50 seconds at 800W.
