It's possible to do it, or to pipe in a more modern radiator to the existing system. You can even buy fittings to convert between gun barrel and copper pipe sizes.
The main problem is gun barrel only has an expected life of about 35 years, as the pipes start to rust from the inside. Systems can last much longer without any leaks, especially if it's a completely sealed system, but once they start you're in trouble.
People don't like touching them as they invariably lead to lots of unforseen trouble. And if it starts to leak next year, they'll get blamed.
For a bathroom, would they consider an electric heating solution? I'm planning a renovation here and looking at electric options that can be put on a timer completely independent of the main heating system. You can even get underfloor that way, or heated towel rails, etc. I like the idea of stepping out of a shower onto a warm floor.