Battery propulsion doesn't need to get anywhere near the energy density of fossil fuels in order to have equal utility, due to the huge difference in efficiency (both theoretical and practical). Ignoring utility and just thinking pure kWh for a moment, do you have a source for your 100-200 year claim, assuming maximum Carnot efficiency for fossil and 100% efficiency in electric motor conversion?

From my armchair perspective, the Tesla Model S would be equally useful to any gasoline car for all but a handful of edge use cases, with only the minor change of adding a metal-air battery as a range extender for excessively long trips. And that's today, not 100 years from now.

Arguably, Bill Gates has more than "a lot" of y intercept.

The saying also deserves an addendum: "... if you've got the time."