We don't need improvements at a rate that is anywhere near Moore's law. Moore's law is about doubling transistor density every two years. But for EVs to reach that kind of ranges (7-800 km for mid range price) we just need to add 50-60 percent or so one time, and I'm talking about that happening in 4-5 years. For the cheap EVs that currently have a range of around 3-400 km we need to double one time. I suggest we will get there in less than 10 years and that is not even taking into consideration the fact that prices on batteries keep dropping.
A "modest" 5-10 percent improvement like we've seen historically, for another 7-10 years, and we have more or less doubled the energy density of batteries. Plenty for EVs to beat combustion engine cars.
https://www.economist.com/blogs/graphicdetail/2017/08/daily-...
https://www.quora.com/Is-it-true-that-battery-energy-density...