I fact-checked this and it turns out I was completely wrong, and I'm sorry. Even with the current grid mix, a typical all-electric car will on average be greener than a gasoline car after about 15,000 miles. Even if you're in a place where 100% of your electricity comes from coal, the electric would still beat out the gas car after 89,000 miles.

So, it is like you said: It is already cleaner, and will get even cleaner as the grid improves.

Thank you for the heads-up! I stand corrected :)

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Sources...

Breakeven points: https://www.reuters.com/business/autos-transportation/lifeti...

State-by-comparisons between electric, hybrid, and gas: https://afdc.energy.gov/vehicles/electric_emissions.html