Actually, I’m more interested in what went wrong with the supposed shut-off systems that are designed to prevent oil leaks following such problems on the surface.

There are plenty of things that can go wrong on an oil rig causing explosions, but there were various safety systems in place (or could be in place) to shut the flow from the well. Those systems - the blowout-preventer - apparently failed - possibly because of the explosion or other reasons.

Several foreign countries have a remote system (an acoustic based system) to shut down the wellhead but the US doesn’t require that type of system and the oil companies have said that that system is unproven.