The grid doesn't have to be 100% green for it to be better than everyone burning gas in their cars. An electric car becomes greener as the grid becomes greener, a gas car is just as dirty today as it was last year.
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.