That sounds like an interesting engineering challenge! Assuming we have a stove with a fast-acting heat source (e.g. induction) and high-frequency thermometer (> 1 Hz), what can we learn about the contents of the pot/pan?

I'm thinking: dump a set amount of energy into the pan (say, 0.5 seconds at "power boost" level), then watch the thermometer. Do it several times, with varying pulse lengths (say, 0.1 to 1 second - you don't want to burn anything on the pan, nor wait too long for it to cool down). This should give you a good idea of the pan's step and impulse response, and - I think - you could guesstimate what its contents are - particularly, if there are any liquids in it, and what they are. Then, continue with normal cooking, but keep a continuous record of power output vs. temperature measurement, and possibly occasionally pause and do a round of such pulse tests again.

I see no obvious reason this wouldn't give a stove quite good control authority even in the presence of liquids, including those that are added or naturally seep out during cooking. I also don't expect any of the appliance companies to ever include this level of sophistication in their products.

I find it very convenient. It's not perfect, because of course a sensor looking at the bottom of a pan can't be, but in practice we've found it very handy for the boil function (bring water to a boil @ 100 deg, drop back to 95 and hold there; making candy/fudge that requires holding around 80 degrees, making proper custard for things like creme caramel. The higher temperatures are good for things like dealing with meats, since I can dial in a temp and not fuss over what's going on.

The thing that has surprised me is how relaxing it is to use - as I say, I feel as though I'm fussing over what I'm cooking less.

That said, they're accurate to only 5 degree increments at best, and I wouldn't try using them for something like a sous-vide replacement.