Range is still a bit of an issue, even if you're just doing touch & go's at your local field. You need 1 hour endurance for the lesson, 15-30 minutes alternate fuel (in case you have to divert), and 15 minutes emergency fuel (normally 45 mins, but EASA issued a waiver for electric aircraft). In practice you want an aircraft with at least 2 hours "trip fuel" (the portion used for the planned flight), so that student pilots can complete the cross-country solo flight they are required to fly. Only now are we starting to see some electric aircraft that have the battery capacity for that.
Then there's the recharging. At the flight school I attended, the airplanes would typically go up 4 times on busy days, sometimes 5. With recharging, that drops to 2-3 flights a day (you're not draining the battery completely on each flight). But if operating costs for electric planes are significantly lower, perhaps having a few extra planes might turn out to be economical... but it does mean you can't pass that savings on to your students.