We had a covered radiator for years
it had a fan in the bottom, with speed control, and two thermostats, one on the water pipe, and one measuring air temperature so the fan would only run when the radiator was hot, and also only when the room needed heating.
The matrix was more like a car heater, mat black and with loads of fins, it was rather small for the 3 kW output, and the water flow was never stopped, with a micro bore system with a non modulating boiler this was not a problem.
You can still buy a version today, improved as one would expect, the iVector has a automatic 5 speed fan, and the speed is reduced as the room heats up, and until non fan assisted it does not really matter where mounted so can be used to both heat and cool, the latter of course needs a pump to get rid of condensate, and for cooling the pipes must be lagged, again to stop condensate damage.
However the modern condensating boiler uses the return water to work out what modulation is required, so a radiator returning hot water due to fans not running will cause the boiler to close down.
With the series system used in old schools and collages this is not a problem, in fact it can be used as an advantage, key rooms fed first, then lesser important rooms i.e. upstairs in bedrooms, fed nearer to the return point, and even with one odd radiator like a plinth heater in the kitchen, having just one likely the boiler will still be happy with a parallel piping system.
I did experiment with the idea of a fan in mothers house, but the size of fan required is quite small, fitting a thermostat to the return pipe was my idea, so once return pipe hot the fan would run, idea may have been good, but the fan was too big, so when it started radiator got cold, so it was on/off all the time.
There are add ons
to try and turn a standard radiator into a fan assisted radiator, the output of the first on is adjustable 2 watt the power supply has a range of voltages
so you can reduce the speed, and with a fan you could box in and the radiator and TRV will likely still work, it seems they use cooling fans normally used to cool computers, so suppose you could make your own.
If it were me I would use an inkbird 308 or similar to control fan, simply as I already have them to brew beer with, but really needs some thing like this
is needed to turn fan on only when radiator is hot. I would also paint radiator mat black before boxing it in, as that colour radiators heat better. As to room temperature control you can get TRV's with a remote sensor
so there is no real need to set it to max setting. Think I would put the TRV outside the enclosure so can still use a smart TRV head.