I am not thinking F1 becomes FE. I am suggesting F1 operates the way it is, but with electric motors instead of petrol. Single chassis, similar race duration, similar pitstops to change batteries and tires. Electric motor could be homologated maybe if people feel strongly about that. Yes you would lose the sound, but then this obsession with sound of engines will seem like an anachronism 10 years from now, and you can always simulate sound like the Porsche Taycan does.
Don't get me wrong, I love sound too. I've had some very nice sounding cars - Jaguar F-Type R, Audi R8 V10, BMW M5, a couple of Porsches. I was brought up with the idea of cars are meant to make engine sounds. When I drive an electric car, I don't miss it. It is just a different driving experience, but not lesser. I also don't miss the sound of the V10s in F1 - in fact I can't remember the difference.