Perhaps this is already known, but I would think there is a high chance that our brains require "write access" to function. That is, the very process of neural activity inherently makes modifications to the underlying structure.
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?