When BR was operating everything the case against MUs was much stronger. There was a resistance to investing large sums in having expensive MUs standing idle all day except just a couple of trips in the peaks. The answer to this was to have LHCS for peak extras using locos that would spend the rest of the day on freights, parcels, PW work or whatever. Typical of this were the peak extras from London Bridge to East Grinstead/Uckfield that were 33 hauled. Likewise the Kensington Olympia service was once peak time only and was two coaches hauled by a 73 on diesel power. This is what is meant I think by saying that LHCS provides greater flexibility to add coaches to services during the peak.
The disappearance of parcels traffic and local freights, and the ownership structure of the railways today, means that the railway operators couldn't just move locos from one type of traffic to another even if they had them, although a flavour of this can be seen in the Fife Circle extras where the skips are free to do other stuff during the day,