Only thing is they should charge more for heavier and for less eco-friendly cars.
Incentivizing eco-friendly cars is great in general, but I think the two concerns in this case are best addressed separately.
Going from 1 person of 200lb to 4 people totaling 800lb (in a 4,000lb car) increases the damage by less than an additional car (4,800 / 4,200) ^ 4 = 1.71
[1]: https://finance.yahoo.com/news/average-car-weight-140033718....
Seems like it would help a lot.
e-bikes are fine though, and should in fact be encouraged somehow. They're a great form of personal transport in a dense city; they're very very common here in Tokyo these days.