Is this definitely correct? OK it's of little use on some of the IC lines under discussion here, but the ex-Southern Region lines definitely seemed to only press units into service during the peaks. Many off-peak services well into privatisation (I'd give the 1997/98 timetable on SWT as an example) were only 4-car off peak, when they were often 12 during the peak. Or, the 442 services to Weymouth were frequently 5-car off-peak, but would be 10-car during Summer Saturdays. The extra stock was sometimes employed on "seaside specials" from the London area during the summer season, particularly Summer Saturdays.
Even though a "Southern" EMU would be little use on the MML or WCML (!), the point I'm trying to make is that there are historical examples of multiple units only being used at peak times, not just loco-hauled MkI stock, so there seems to me to no reason why you can't have MUs being pressed into service at peak times just because they are MUs and not hauled stock.
As for not wishing MUs to sit around idle for months, this would not happen as the peak-only units would be needed for the Mon-Fri commuter peak, and then could be re-used for weekend peak periods.
I will agree that the fragmented railway has made such things more difficult. Re-unifying the railway in some shape or form, whether it be private or public, and simplifying the structure (goodbye ROSCOs, for one) would help, I feel.