The utilization factor would obviously be much lower than it would be if everybody charges at a lower rate so if the total amount of energy is equal that just means that individual vehicles will spend less time charging, and the grid will see - roughly - identical utilization on average but the peaks may be higher.
Probably worth pointing out that the peaks and troughs are what are challenging to deal with. Generators aren't generally great at changing output super fast.
I keep hearing battery tech is getting good, and the research I've seen suggests that more storage on the grid would improve efficiency by a lot, so I don't know if it would even pose a particular challenge if that sort of demand arose.. but overall utilization isn't really the limiting reagent.
