No that’s not how they actually operate and are perceived. You’re so used to losing a huge amount of heat through your feet warm floors feel amazing.

No, a whole house system can (and should) have floor thermostat elements for precisely this reason. Cycling an underfloor heating system on ambient air temperature alone with a naive (non PID) controller leads to these type of issues.

A stable underfloor heating system will have the floor at a constant temperature slightly above the desired ambient air temperature. Heat losses in the house lead to a steady state equilibrium. You can do that with an expensive controller and an ambient air sensor, or a cheap controller and a floor sensor. A cheap controller and an air sensor, like this case, will over and undershoot and be miserable. This can be moderated by high thermal mass systems but is not eliminated.

The problem here is how it’s being controlled, not any fundamental failure of underfloor heating.