The question is how should it work? OK, my house is a bit on the large size, but the idea of one device turning boiler on/off, does not work. Forgetting my flat, under the main house, the main house has 3 devices which can trigger the boiler.
We can adjust heat-up times, with the lock shield valves, but we can't control cool-down times. So the TRV in general stops over-heating, and the wall thermostat stops under heating. Although, we can link TRV heads if required.
As to domestic hot water, a cylinder of hot water can last 3 days, and it costs to fire a boiler, so in general want the DHW heating while the CH is running as well, so you do not heat the boiler to produce just enough hot water to wash your hands. It seems odd, but in many ways one of the oldest systems was the best economy wise, the old C Plan had a lot going for it in the winter.
But to consider faults, first one must look at the system used. Honeywell gave the systems letters, the C, S, W, Y, etc. The W normally inside the boiler where the reservoir is built into it. The Y uses a three port valve, the S uses 2 two port valves, and the C does not need any valves, but my C Plan has 2 two port valves, so counting the valves can be miss-leading.
So Tado, Tapo, Honeywell Evo home, Drayton Wiser, and Hive, all allow TRV heads to connect to some central unit, which has a verity of names assigned to it, so the TRV heads can both stop over and under heating. In some the central unit is a simple hub, in others it doubles as a thermostat. There are also ways to control TRV heads from remote heat sensors, so where the TRV is in a draft, it can be controlled by a device not in the draft, but also the draft can be used to detect when doors are opened and inhibit the radiator for a set time, so it is not heating outside when unloading a car for example.
Cost of TRV heads and wall thermostats varies a lot, so where two rooms have nearly the same conditions, one may have a full-blown linked electronic TRV head, and the other a cheaper non-linked head.
So in my case if the wife's bedroom gets too cold, the TRV head can start the boiler running, but in my bedroom the TRV head can allow the radiator to heat up if boiler already running, but can't start the boiler. Both are electronic with different temperatures for different times of the day.
So the way central heating controls heat in the home varies, some people don't have any TRV's, some have only mechanical, some have electronic programmable unlinked, some have electronic linked direct, some have electronic linked to a wall thermostat, so many options.
My house was a mess, and it took some time to get it working as I want, it is a compromise, my boiler is simple on/off oil fired, gas boilers can often modulate, and gain the latent heat from flue gases, so in general three ways to control a boiler.
1) On/off device, be it thermostat, programmer or combination using electric to control.
2) Up/down device, otherwise as above, but connects to ebus, OpenTherm is likely most popular way.
3) Return water temperature, this relies on the by-pass valve, lock shield valve, and TRV being set correctly.
The third and the first two can be combined, the aim with a modulating boiler is to reduce how often it is switched off and on again, each time it is switched off and on, it has to work out how much to modulate the output from scratch, and it also often has a cool down function, where each time switched off, it continues to run pumps etc, for short time, the same on switch on, where it runs a purge first, so where we can, we want analogue control. With central heating in general, on/off (digital) is bad, up/down (analogue) is good.