I wonder if cities will also start designating streets (or as a softer approach, significant amounts of parking) as EV-only.

A city that wants to electrify the vehicles driving there could do that very easily by converting a certain percentage of parking spots to EV-only every year. This will roughly ensure (at least) the same percentage of cars in the city being EVs (since if there's more, using a non-EV becomes extremely unattractive as you can't find parking).