Ironically, this whole crisis was caused because they did precisely that—the reactors shut down automatically for safety reasons, and then they had no power with which to keep the pumps running because the diesel generators were underwater. Had pretty much any one those reactors not automatically scrammed, it is likely that things would be in better shape than they are now.
Thank you Captain Hind Sight, BUT
Not sure how a runaway critical reaction is a better outcome than the current situation. If the SCRAM units did not kick in, the reactors would remain critical, and the state of the rest of the plant would be unknown. What happens if the quake knocks the control rods out of alignment, or disrupts the turbines that generate the power, or bends/cracks/breaks the coolant lines? With a critical reactor the designed power output is up in the 1.1GW range, anything going wrong that could disrupt the cooling systems gives that power nowhere to go, and 1.1GW (or more, if the reaction does actually run away) is a whole bunch of power to concentrate in one spot. SCRAM units take a maximum of 4 seconds to fully insert the rods to stop the reaction, leaving little time for anything else to break and prevent their use. It was the 100% correct thing to do. Even IF the tsunami didnt wipe out the generators AND POWERLINES (remember, it took them over a week to run a new powerline to the plant) between the plants, and one stayed operational, running pumps with nothing in them to pump does little good (cracked cooling line/evaporated coolant/steam releases), as does powering broken pumps or pumping coolant through broken lines (they still arent sure the pumps or lines are operational in some of the buildings).
What went wrong, besides under-designing the seismic and tsunami resistance of the plant, was placing the generators in a position where a tsunami could wipe them out. Had they been on the roof, or on/in an elevated structure (like the top floor of the reactor building itself??) and as protected as the rest of the facility they probably would have remained operational, and kept the coolant flowing long enough to get mains power back without anything reaching any worrisome state.
Newer fail-safe reactor designs are in evaluation as this is all happening. It takes YEARS to get anything rolling with these plants, you cant just switch them out one day. It is the goal to replace the old ones, it just takes time and lots of $$.