A good room sensor by itself cannot "measure how the house responds". The compensator needs two points of reference. The others is the outside temperature.
Of course it can.
The system knows the time. If eg it's cooler in the house than it was yesterday just before the heating comes on, it knows it's going to need more power to heat up by the set time. The outside temperature is a derivable paramater not a principal one.
Remember the boiler's also already measuring the return temperature, or should be, too.
Outside temp also doesn't take account of sun wind or rain, opening windows, people in the house, the oven etc etc etc. Outside temp control is an open loop control which introduces all sorts of errors which have to be fudged over, or corrected.
If your train lurched the loop parameters were wrong. Loop gain, damping factor, loop delay and so on.
In a house, the temperature sensor is way more sensitive than a human - it knows there's a change well before you do.
A normal PID control system can predict very well how a system will respond - "learning" algorithms have been around a long time - well before I was writing my own in the 70's.
Feed forward control can't avoid producing an over/undershoot error, depending on the inertia in the system.
The grail isn't even internal room temperature, it's comfort. Some people expect the inside temp be lower in the winter and want it that way because they get used to it. Other houses have so many cold spots that the average temp has to be higher for sensitive people. Comfort can be made up from air temperature and radiation from a hot radiator.
This and more is all stuff which means the occupier is more likely to feel out of control with a "clever" system.
System needs a decent room sensor and decent software, that's all, with a knob on the front you can turn in stages, marked "For Simple People" at one end and "For SmartAsses" at the other!
Commercial requirements, btw, are different - for reasons I won't go into here.
When weather compensators came in, it was BEFORE the boss of ICL stated that there would never be a need for a computer in a house. Times have changed.