One reason to run the batteries in parallel is that the slower the rate
at which you discharge a battery, the more total power you can get from
it. I.e. if you discharge a battery at 1 amp it will not deliver as
many amp hours than if you discarge it at 0.5 amps. This is somewhat
offset by the need ( or good idea) to isolate the batteries with low
loss zener diodes. The 0.25 volt drop of the zeners means that in
effect you can only discharge you batteries to 11.25 rather than to 11
volts - which sacrifices some capacity. You have to get out the data
sheets for the diodes and batteries to see if this is a good tradeoff.

I believe that using one battery switch rather than multiple spst
switches is a bad idea because the single switch becomes a single point
of failure. Having 15 batteries is of no value if the switch breaks.