Typical UX design by an engineer as it is, with wrong assumptions about user expectations. The users of microwaves do not want to heat something to 100 degrees. They either want warm food or they want to cook. Warming means, that not only surface temperature measured by sensors has to be comfortable, but the temperature of the whole meal, which depends on thermal conductivity and penetration depth of microwaves for specific food and cannot be controlled by a sensor array alone. People will just hit "start" again, if they feel it's not ready.

For cooking people will either use recipe from a book provided with microwave and thus they need just a selection of a program, or they will use more advanced microwave with oven and will want to set temperature of the oven to something like 200 degrees for 40 minutes. In this case sensor would be useful, but it's already not a microwave story.

Isn't this just you projecting the limitations of current technology on an effort to improve it though?

Users of a microwave currently expect extremely poor temperature control, and so don't even think about temperature because you get what you get. An interface which lets me heat something to exactly "drinkable but hot" is a revolutionary change in how I use the appliance though.

Same story with warming food: sure, you want it warm all the way through - if you actually know the surface temperature though, then you can model that - food that is cold inside is going to have different surface temperature decay rates to food which is warm inside, and some modeling of the observed thermodynamics means the appliance can know this.

So now we'd really be talking: "warm to safe temperature all the way through" and we can give a probability / % complete read out of how close we think we are to it. No more guessing, no more user interaction, also no burning yourself because some parts went superheated.

Theoretically speaking, you are right, and at some level of technology it might be possible to implement this. However, "drinkable but hot" setting is quite far from "surface temperature at 100 degrees", right?

The problem is that this forces you to make a confusing decision right at the start. You almost never know what temperature to heat something to -- you just want to put it in the oven for 30 seconds, see if it's good enough, and then repeat.

Or a problem solved by sane defaults: i.e. 65ish degrees is quite hot, whereas 55 is about the upper limit of long-term bearable on the skin.

Put that option as the heating default, with literally what I just wrote explaining it next to it, and problem solved.