> a high chance that our brains require "write access" to function

There are multiple learning mechanisms that happen on different time-frames, eg neural plasticity, hippocampus are both longer-term processes for memory consolidation. Whereas the content of “RAM” might be better modeled as a set of fast dynamic weights representing ions and neurotransmitter concentrations.

My hunch is that you could model the latter fast weights in volatile memory, but I wouldn’t count these as “modifying the structure”.

Do you have any particular systems in mind where you have reason to believe that permanent modification is required for brains to function?