This is how the theory works, and greatly over-simplified to show the point:
Though both operate while we are conscious, the sympathetic nervous system controls most of our responses including “fight or flight.” Because it acts protectively, it tends to be an erection dampener (sort of “unsympathetic” to erections occuring). There are good reasons for this. At or jobs (or hunting in the forest for mammoths) it would be inappropriate to have erections because we could damage our penises, for one thing, when running through brush with spears in our hands, hence most of the time while awake, we are flaccid, unless sexual impulses are sufficient to overcome the erection-dampening effect.
During REM sleep, the sympathetic nervous system is closed down and the parasympathetic takes over. Without the sympathetic saying “NO!” most of the time, the parasympathetic is free to encourage erections, and frequently. Nocturnal erections then occur in a normal, healthy male without ED 4 - 5 times during REM sleep and are sustained for about a half hour each. There are no impulses at all from the sympathetic system to hold them back. It makes sense to me that the larger size many notice in these waking erections from REM sleep might be attributable to no interference from the sympathetic nervous system.