If people get home from work, and immediately start charging their electric car, turn on their heat pump to warm up the house and start cooking dinner on their electric cooker then that will just be adding more demand at what is already the peak time of day.Furthermore these changes will probably markedly alter the timing of 'peak' periods
It seems clear to me that some kind of scheme is needed to incentivize matching demand to supply, but I'm no expert on the details of how that can best be made to work. "Agile Octopus" uses a system where pricing is based on "day ahead" wholesale rates but the problem I see with that is it could cause everyone to dogpile on whichever hour happens to be cheapest.
Perhaps a tariff where you get a set number of hours each day at each price, but the supplier determines which hours have which prices (and can assign different cheap hours to different customers to balance load).