Disclaimer: Just a wild guess. Conspiracy theory to follow 😉
With the amount of liability money at stake, the public is not going to know the true facts for a long time.
My guess is the rig received a larger than normal kick from the well and it actually damaged the casing below the BOP. So even if the BOP was activated ( may well have worked but later opened due to erosion around the casing ) the extreme pressure may well allow hydrocarbons to escape around the casing further damaging the well.
So, the only real solution is the relief well to relieve the pressure and pump cement into sound rock to plug the original bore. But that will take 45days at a min. BP has a public relations problem and nobody would buy them saying it has to flow for 45 days before it can be stopped. Hence the daily top kill progress reports.
I am surprised no one has proposed:
1. Activating this well and designation all of its profits for cleanup and future cleanup fund.
2. Drill many other wells next to it as they have found a great source of oil.
3. Why didn’t any regulatory agencies require booms around the rig during the fire? They didn’t know of the leak at that point (maybe) but for the oil that was washed overboard during the firefighting.