Westy
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That is literally impossible. The main reason that some people continually write about the "school run" effect is that they fail to appreciate what is actually happening during the school holidays - which is a LOT more than just schoolchildren not being driven to school. The school holiday effect is not just "the absence of the school run"; it is also the absence of a great many other things that happen during term-time but not during the school holidays. See other recent threads on that very topic.
Its effect is likely to be limited, but it's still worthwhile.
I buttume "make the prices less unattractive". It might even make a marginal difference. It won't make a big one because price isn't the only consideration.
How?
This is an interesting one.
One of the main attractions of car-use (or motor-bike or push-bike use) is that it is completely flexible for the user, with no timetables to adhere to and no critical failures because one happens to be at a particular geographical spot a few seconds after an arbitrary time set by others. It certainly isn't the whole story, but it's a significant part of it - and even if not too often vocalised by drivers, they soon notice the difference if they switch (whether for a temporary period or indefinitely) to public transport. Once one acclimatised to not being regimented, going back to it is not easy at all. Car-sharing sounds nice in theory, but it has one of the bad effects of switching to public transport, which is the imposition of the tyranny of the clock and the timetable. There are one or two other disadvantages, like everyone in the car having to leave for home at the same time, thus limiting flexibility in working hours.
It isn't, but it is quite a bit more complex than you seem to think.