If I am not missing some details here, that is the standard way of heating rooms, given that floor heating is still not so common. On the spot I would say that the costs depend on how you heat the water, not much on the elements - they just transfer to the air the heat they receive.
We have "Fernwärme" and those elements, I guess it's less expensive than floor heating powered by an old oil burner in the basement.
The image you show looks like an oil filled electric powered radiator as there are no pipes in or out.
With such scant information it’s difficult to tell more. Hot water for showers etc and radiator heating are usually on separate circuits, water for radiators being sealed.
Turning off at night may save a fortune or not much at all depending on insulation and set room temperature how many radiators etc etc...
I live in a rented apartment. Very much of the costs of heating, cooking etc are the fixed costs. Having said that I did save quite a bit installing electronic radiator (like in the picture) controllers so that the heating can be on a timer rather than leaving it on all night. I've also put reflective insulation sheets behind all the radiators.
How much those radiators cost to run depends, of course, on how they're used.
That "just" regulates the flow of hot water, and basically how hot the element will be. The regulation of a single element has IMHO not a huge direct impact on costs, particularly if you are part of a bigger building. However if you keep it always to the maximum it could be that the actual temperature becomes too high and you end up opening the windows to avoid sweating, wasting heat and money.
I always tuned them to the actual room; I started with 3 (or equivalent), then for example I increased to 4 or 5 for the cold room facing north and reduced to the minimum for the room that had hot pipes inside the wall...
Keep in mind that if the central heating has some cycles your regulation will also be affected, e.g. if the boiler generates hot steamy water in the morning you'll sweat at 1... this should not happen, but with old buildings things can be a bit "non optimal".
In my experience the valves here are thermostatic i.e. level 3 corresponds to a particular room temperature. Mine in the UK though are more like you describe.
To try to somehow answer the question, I think it shouldn't be difficult to understand the costs would be higher the more the heating is used. Whether that means you shouldn't have it on much I don't know. You should get a statement of heating costs each year then you can have an idea about actual costs. For me I saw that more than 50% of my heating cost is fixed charges. Unless you live in near poverty it's not something I would worry about. Like I said, consider getting the electronic programmable controllers if you think heating a room at night is a waste.