You have not enough respect for those little thermostatic valves!
Yes, they are near the radiator. Yes, this will have a slight effect. If you don't like that, get one with an remote sensing element. They exist! Fully passive!
No, they won't turn off because it's over 22 degree. They are
a lot slower than that. True, tuning them is tricky, but so is a DIY PID solution.
Thermostats are not simple on/off devices anymore.
Also, the radiator will create natural airflow, which will provide airflow around the sensor. You shouldn't place things on top the radiators, such as desks.
...
If you have a boiler that supports it AND you only need ONE temperature to satisfy ONE demand.
Also I'm fairly sure that very, very few smart thermostats support that and I know that most boiler do not.
There is an approach which I know people use which it to turn the heating temperature way down and leave the heating on, much much longer. However this is bit of a damp squid when you consider how much electric a boiler and circulation pump uses.
Yes, the heater needs to support it. I don't know about what heaters are common abroad, but here Nefit and Remeha gas heater are supporting this for decades. It's called modulating.
Also yes, the thermostat must support this. Usually one comes with the heater, otherwise a Honeywell Lyric or Nest will help you.
The cost of heating water electrically does not change. Pipe loss maybe, but the energy is the same. The heater is inside your house, so theoretically 100% efficient. The loss will be in the insulation around your boiler.
...
if you lower the water temperature won't the valve just open more?
The valve will open longer. If your house is sufficiently insulated the frequency of temperature instability will be lower, and you will be closer to the requested temperature. More comfort.
If you're pumping 60C water through the radiators every 30 minutes it will be degrees over, then degrees under the requested temperature. When the same temperature can be maintained by pumping say 40C for a while as well. For gas heaters, this is cheaper.