You don't use steam for district heating. There are two problems here, the first one is that district heating doesn't exist in a lot of places so the infrastructure needs to be built. The second problem is that people are afraid of nuclear so running water through their house warmed almost directly with nuclear heat is a sensitive topic. It's not actually dangerous of course, but perception matters. Actually there is a third reason now that I think of it. Nuclear plants are usually not close to big enough cities to absorb that heat, but it's possible to transport the water over 100km while still retaining enough heat for district heating.

Some district heating systems do in fact use steam.