The keyword for the problem you're talking about is the "long tailpipe theory." [1] I was just reading Wait But Why's article [2], which concluded that the overall greenhouse impact will still be lessened by using electric cars over internal combustion.
I didn't dig into the sources enough to conclude that it's truly a better option, but those articles are a good place to start.
It's not really a fixed cost. Batteries aren't good for forever. They have a limited lifespan.
An electric car could be thought of as a gas car with a very, very large, magical fuel tank. If a battery costs $20k (like a Tesla) and I spend $200/mo on gasoline then that's 100 months (simple interest) or about 8 years, before we even talk about the cost of the car or the cost of the electricity.
I know that this doesn't feel good to talk about, but economics is more about numbers than feelings.
That economic analysis is flawed because you're ignoring the externalities of burning gasoline (health costs, climate change). Only if there were high enough taxes on gasoline to mitigate those effects, then you could accurately do that sort of dollar-cost analysis.
Sure but then every analysis is flawed because everything has some kind of externality that's hard to measure and account for.
How much fuel is burned to make the cells? How much pollution happens to mine the rare earths for the cells and the motors? It's super easy to poke holes in both sides of the argument because building a car is so damn complicated whether it's an ICE or electric.