In the UK, many homes and older office buildings still have traditional bi-metal mechanical thermostats. For typical domestic applications they work just fine.

For finer control of room temps, people often use mechanical radiator thermostats. They work just fine too.

New electronic models are usually just a thermistor with some analogue hysteresis. They work fine as well.

I might expect something with the extras you're describing to appear in a new office building, but in the UK at least adding PID and/or some kind of learning system to a domestic thermostat is overkill.

Generally, simple solutions are less likely to go badly wrong.

That's the tragic irony of Nest. The design is great, but the added value offered by a buggy and overcomplex implementation is negative.

In home systems aren't most of those problems handled by the furnace/ac system itself? Thermostats are pretty dumb.

Depends on the hardware. An old-fashioned bimetallic strip/mercury switch thermostat has mechanical hysteresis built in. (Actually, they can have too much lag -- some of them include heating elements to 'accelerate' their response.) Old-school mechanical devices aren't always as dumb as they look.

As far as short-cycling the compressor goes, my current HVAC is smart enough to disallow that, but I've lived in older houses where that wasn't the case. You could potentially damage the compressor by wiggling the thermostat back and forth, forcing it to start up against back pressure.

Understanding the requirements is really job #1, and first on the list of reasons why HVAC control isn't just a simple "if too cold then turn on heat else turn on A/C" statement. That doesn't mean people shouldn't jump in and try it, of course. It's the best way to learn, if not always the cheapest.