@Lyman
To my knowledge, the Ship's and APU batteries for the 787 power the same systems as they do on other Boeing Commercial Airplane families. So I don't believe Boeing is asking more of them on the 787 than, say, the 777.
As to reliability issues, I agree that the containment box does nothing to address this. It's merely designed to ensure that if a battery enters thermal runway, it cannot affect the safety of flight of the aircraft.
To address reliability, Boeing is making changes to the battery design, increasing cell spacing and putting in insulation between the cells. The expectation is that this will reduce the chance of a single cell entering thermal runway and, if it should, reduce the chance of adjacent cells entering thermal runway. They also appear to be increasing quality control in production of the cells and assembly of those cells into batteries to reduce the chance of a short circuit that could induce a thermal runway in a cell.
Even if Boeing eliminates safety as a concern, they must also eliminate economics as a concern. As the APU battery appears to be necessary in order to run the APU, the low MTBF for the APU battery is going to affect the ability to certify the 787 for ETOPS beyond 180 minutes (the current limit for a plane with an inoperative APU). And even if a failed battery can't damage the plane, it is expensive to replace so a low MTBF will be a concern and pain point for airline customers.