Can anyone explain what is wrong with the hypothesis of a largely structural long-term memory store? (i.e., in the synaptome, relying not on individual macromolecules but on the ability of a graph of neurons and synapses to store information)
There's nothing wrong with it, it's just that the strength of connections (local synaptic concentration of various neurotransmitters and receptors) has been demonstrated to be just as important as their graph-theoretical structure for long-term memory. Synapses can regulate their strength and maintain the strength over long time periods. The problem that the quoted paragraph is trying to illustrate is that a simple chemical concentration explanation doesn't cut it since chemicals are being diffused and turned over inside synapses all the time. Thus there must be some mechanism for long-term persistence of memory.