Everyone pays. If you want to come up with a method for EVs to pay their fair share, without some government thug tracking your movements or requiring yearly mileage inspections, I'm all ears.
If I was King Yota, and it was up to me to decide what would power us for the next 100 years, we'd be building a hundred nuke plants per year and make power meters obsolete.
The reality is that generating power will be like it is now, a mix of lots of things. Coal and natural gas plants, hydro, nuclear, and a smattering of renewables here and there. As home battery banks become larger, cheaper, and more common, decentralized generation using solar panels and whatnot will take over for residential power and EV charging.