Almost the entirety of safety issues with existing reactors is around cooling them. Bad things happen when you can't cool them.
There's many ways in which this can happen in existing reactors. You may have a catastrophic leak and lose the coolant - and you can't just send some welders in, what with radiation, superheated steam etc. The pumps that push the coolant around might fail. Etc. etc.
Even when you "switch off" the chain reaction, the fuel rods keep emitting heat from the decay of transient radioactive elements, enough to need active cooling for days or weeks.
So a lot of new reactor designs revolve around eliminating such failure modes. NuScale for example, IIRC, don't use pumps to circulate the coolant, and that's one thing less that can break.
What I'm daydreaming about simply cannot stop working, in terms of cooling. You have something hot in the middle, you let all the heat get our naturally, and you harvest some of it along the way.