1 - How to bill people for their electrical usage
2 - How to get everyone onboard. There would be so much opposition from so many sides simply because they want to maintain their livelyhood. Car mechanics, auto producers, gas companies, service stations and so on.
As for how to get everyone on board... it would not be easy. IMO the only way to do it would be gradually building political support... rises in gas taxes, etc. Get trackless trolleys (elec-buses) using a system first, and then open it to private vehicles later.
Overhead wires such as those used by some seattle buses would probably be a lot cheaper to install though. That might make them a lot more likely to get implemented.
If you understand how electric meter enforcement on houses work, it appears that they might be practical on cars and e-bikes too. Essentially, using electricity without a meter (and without getting electrocuted) requires a lot of work... and doing so without everybody nearby being able to see is much, much more difficult... and if you're caught you've committed a serious crime. All electrified roads would be in plain public view and all vehicles using the power would have a registered meter; meters would be presented for mandatory monthly inspection at the electricity-provider's office (or maybe at your home's regularly scheduled meter-reading). Or something like that. I guess stolen vehicles would operate for free until caught (!) and people might be tempted to claim that their vehicle was stolen. I think installing photographic license plate readers* to help catch anyone trying to use electricity without a paying electric account would solve that problem, though.
Besides taking away the need to purchase and carry batteries, systems like this (as used today on public transit or as modified for private vehicles) mean that you don't lose energy charging your battery and then again discharging the battery, which collectively avoids a huge amount of energy loss.
*like the ones used to give speeding tickets in some locations