Have you practiced control theory in an actual process plant? PID is not simple to tune it at all, well PI, nobody uses the derivative part. Countless studies published in the industry show that up to 30% of the PID control loops in operation are set to MANUAL by the operators and from the rest more than half have wrong parameters.Even then +90% of the controllers are PID, because despite all their problems they work better than the more sophisticated alternatives, they are more reliable, maintainable and cheaper to license.

> PID will basically have you experience either large overshoots (which you will experience as overcorrecting to changes in demand) or slow adaptation to changes.

Such a blanket statement is meaningless without a description of the system you are controlling, those kind of overshoot can be attributed to wrong parameters, to badly sized elements of control or even to bad measuring devices, the PID algorithm has zero to do with those cases.

> I have implemented a controller for espresso machine boiler water temperature. Replacing PID with moving horizon estimator allowed me to cut time from startup until stable temperature by at least half and eliminate any measurable over or undershoots.

Did you try a "bang-bang" controller,I would no be surprised if you'd get the same results with 1% of the complexity.