The problem was not in shutting down the chain reaction - that worked just fine. The problem was in dealing with fuel rods that were still, due to decay processes that nothing in the universe can stop, producing massive amounts of heat that, without active cooling, would melt them and re-start the chain reaction.
Sure, but if the reactor can go a week without cooling and not sustain damage, you've got a lot more leeway. Some of the GenIII+ designs we have now can do that.
The ultimate solution is probably the molten salt reactor. With liquid fuel you continually remove fission products, and with most of those gone you don't have decay heat issues anymore.
