I do for instance think there's a very strong case to drop Merseyrail to 2tph between the weekday peaks in order to free up money to increase the Sunday shopping day (say 1100-1700) to 4tph, which would be far more in tune with actual demand than what runs now (which has, bar the service beyond Rock Ferry, been basically exactly the same for the last 40 years or so since the base went from 3tph to 4 in the early 80s, and dating back to when Liverpool city centre was basically totally closed on a Sunday and when most families had only one parent working so there was a lot more demand for daytime travel, particularly as families typically only had one car and the husband tended to go to work in it in those days) and could potentially be cost neutral or actually save costs.
As for outer suburban services like around London I suspect those have always been quiet between about 10-3 weekdays outside school holidays as they don't serve much of a local travel purpose - the mentality in the South East is firmly that trains are for going to London and buses and cars are for local travel.