Doesn't burning nuclear waste just turn it into a gas or a pile of ash with the same radioactive elements? Burning is a chemical reaction, so the actual nuclei of the atoms shouldn't be changed at all.
My favorite is mixed design - nuclear fusion core which itself may be even a bit net energy negative (and thus much more realistic in the near future) and which main purpose is to generate neutrons to burn pretty much anything "heavy" and cheap. Turn the power to the core off - the thing just stops.