> here with new thing ones you want to heat up the air so you don't want radiator to be warm but air in well insulated building.
This is more complicated than this, and the construction industry has actually gone back and forth on this topic for the past 40 years. A few consideration against your point:
- When you heat air, you dry it up, which can be pretty uncomfortable for the inhabitants.
- Air stratification is a big concern: when you heat air up, it raises up to the ceiling, warming nobody but the spiders in the corners. It's not uncommon to have a multiple Celsius degree difference between floor and ceiling, even in an air-tight room.
- A house cannot be air-tight because you need to bring new air for breathing, but also to avoid excess moisture in wet rooms, which means your precious warmed-up air is being vented away, and you bring cold air from outside instead. There exists sophisticated systems with heat exchangers to collect heat from the outgoing air and warm the incoming air, but those are really expensive and far from ubiquitous.
- Under standard conditions, thermal comfort comes in roughly equal part from the radiative flux (from the walls) and conduction/convection (from the air) one. So you can achieve a similar level of comfort with lower air temperature when you have a warm radiative surface in a room.
At the end of the day, old cast-iron radiators are pretty good from a heating standpoint. (But they have multiple drawbacks, like being really big, and so heavy you can't move them when you want to refresh the room paint, etc. which means that nowadays, people usually prefer underfloor heating instead)