My father did that a long time ago in a house that had baseboard heat. Made a fire grate out of plumbing pipe, ran the baseboard water through that. It worked, when it did. It would also somehow get air in the lines and start banging from time-to-time. I was a kid, so I don't know if the monetary savings offset the pain in the arse, or not.
In parts of Europe (definitely Germany) heating with water based radiators throughout the house is normal. And that goes from individual houses to big apartment complexes (I lived in a 52 unit one with a central furnace). It's totally normal to let the air out of your radiator from time to time. And they (or you in the individual house case) fill up the water in the 'closed' system from time to time.
Different places, different 'customs' i.e. systems we are used to. All have their pros and cons and sometimes it's just that we don't know that different systems exist.
Radiative heat actually makes you feel significantly warmer, so you can set your heating to a lower temperature and still feel the same warmth compared to airflow heating. This is the reason why floor heating is very efficient, because you have a large heat mass with radiative heat that sits at your feet (which typically get cold first). So it provides the same comfortlevel at significantly lower temperature.
Which is why it is better to make a quick but strong draft in your home than keep window constantly slightly open. With a quick exchange of air, your walls remain warm and continue to radiate heat. Having a window constantly slightly open means air exchange is slow but constant and the area of the wall around the window cools down significantly.
