Your comment of how sensitive the control devices are is very important. I worked in a garage, doors opened so often the heating selected was inferred, however near impossible to regulate. Switch off cold, switch on warm, in seconds, any idea of a thermostat was out, as they did not warm air directly.
If you can combine air heating with inferred then you can keep the air at say 16°C add the inferred which gives one the feel of being in a room at 20°C. It's all down to how many air changes per day, at say 24 complete air changes per day one would want a low air temperature and a high amount of inferred heating (assuming not using a heat recovery unit.) but at 1 air change a day one could likely get away without any inferred heating.
In theory you could have a LED lamp with a inferred ring around it and a winter/summer switch so in winter only is the heater used. In an electrical heated house, having a low back ground heat and PIR operated inferred heaters could work well, the problem is when we have cheaper heating.
How long a room is occupied also makes a huge difference, a church would likely work well with inferred heating as it would only be used for 3/4 hour three times a day. However it is the control where problem lies, outside at -10°C or 10°C the heaters are the same size, so combined heating works better, church held at 10°C air temperature and the comfort remains static from -10°C to 10°C.
Now I am a bit of a miser, so my house was kept at around 18°C and I got away with this until the tungsten lamps were replaced, now we have the temperature increase to 20°C in the evening as said before, open plan house and a simple programmable thermostat worked well. Mothers house with internal doors was completely different. Sorted now, but it has taken nearly 2 years of trying a selection of ideas to keep rooms at a steady temperature. My mother loves work, she will sit and watch it all day, in her case the LED lighting helped as wanted the same temperature all day.
But mothers house is a good example of the problem, while I lived at home I would see the Pet cam record 27°C and jump in the car to find out what was wrong, also go 14°C and with a 92 year old lady that was not what I wanted. When I came to live with her I found the thermostat was losing radio contact and so could cure it, but did not find this with random visits, it must be the same for any heating engineer, he visits for a hour and has to try and work out what is going on. OK may be they have seen it before, so work it out quicker, but when I started the hunt I found every lock shield valve was wide open, and it would seem the central heating installers had not made any attempt to set up the system.
There must be many homes the same, and with a central heating system heating some rooms to 26°C and other to 16°C any heat from the bulbs would not really be something taken into consideration.