I think this is a non starter (if you wanted to maintain F1 speeds) Formula E takes place on twisty street circuits at a pedestrian pace (compared to an F1 car) and they only just make it to the end of the 45 minutes with a lot of energy saving. If you put a Formula E car on a track like Monza how long would it last at Formula E speeds let alone F1 speeds?
Consider this.
F1 aero is now extremely limited by the strict regulations. Due to the huge power and near unlimited energy, air drag is happily sacrficed for downforce.
Now, with spec hubs and wheels, cars could be limited for a maximum load (mass plus downforce). Let's say, ambient air pressure corrected.
With a modest maximum downforce but more freedom, drag would be vastly reduced. This is vital on long straights.
What lap times would you consider worth watching? As in 1994? Or would you still watch 1985 cars?
With less draggy cars, top speeds would be to anyone's liking. As an example, the iconic McLaren F1 road car from the 90's hit 394 kph or so with maybe 650 hp. And it was way heavier than a BEV F1 would be. Of course, F1 will have shorter straights.
With 3 stops, you get 4 battery discharges for a race. Let's all agree that FE's energy density is decidedly meh. And that FE on the F1 battery would be able to shuffle around for well over an hour. Let alone with more drag focused aero.
FE is also very slow due to the all-weather (good for snow) road tires that barely wear at all. Oh, and downforce seems to be a myth, missing bodywork doesn't cost them pace.
So an F1 car would have 5-6 times the energy of a present dat FE cars, a much more slippery body kit, F1-worthy downforce, wider tires which would be real slicks, etc. This all combined allows for much more power, which leads to good laptimes. With the technology battery company now have in the laboratories, we'd surpass F2 lap times I'm sure. Would you watch our stars in SuperFormala speed cars that are a mix of Group C and F1 in terms of aero looks? On races with some FSCs, some team might risk a pit stop less. Which would be a good half minute on the track. Or, they'd make a late 3rd stop and then stick in a lighter pack with less range. Bang, 3 seconds a lap faster after saving more energy throughout the race, big march to the finish! But in most races, you could use that smaller pack only once, if at all. Apart from Monaco.
BEV F1 cars would basically be better. Move less air around, get downforce from ground effect mostly. A lot of energy regeneration, in part due to slippery aero, resulting high speeds and high-ish weight. Cornering would not be too bad. Today's racing is just insane, no-one ever needed these lateral G's for spectacle.
With heavier, less powerful cars and maximum load per wheel at given speeds, aerodynamicists would have much more play room. FP1 would be for aero setup effectively. Stay under load levels, optimize balance and drag. Cars would probably look very different to come to the same performance level.
Some fear that cars would be too silent, but twice FE would not be whispers.