Oblivious RAM write protection
Surely multiple randomly addressed writes would potentially overwrite critical data...


Nope.  The oblivious RAM data structures take care to ensure that, when doing reads and writes at random locations, they don't mess up the data.  For instance, if doing an extra write, then they make sure to write the same value that was already there (except in encrypted form), so that it doesn't change what value is stored there.


  batching the writes would stop an attacker knowing exactly which addresses were written to at a given time


But the attacker would still know which set of addresses were written, which is leakage of partial information.  Oblivious RAM aims to eliminate even this partial leak.  So oblivious RAM achieves a stronger property than batching could ever provide.