I saw a documentary about Renault doing this in Israel I think. With a network of stations looking like auto wash: it takes your car, opens a door under the car, swaps the battery with a full one and off you go.
Apparently it went bankrupt after a year (2012-2013): https://en.wikipedia.org/wiki/Better_Place_(company)
Not all EVs use the same pack type and there are advantages and disadvantages to the different types that will continue to change as we progress the technology. It wouldn’t make a lot of sense to have universal batteries as it would also limit the designs of the car if it were legislated.
Universal batteries would be bad, but standardized batteries would be great. If a battery has certain dimensions and gives a certain output, and can regulate itself as to charge and discharge, it doesn’t matter what chemistry it uses or internal cells it has. We have had D, C, B, A, AA, AAA, etc., for years and manufacturers got along just fine within those specs. Removable batteries are already a thing with Gogoro scooters in Taiwan and I think at least one car brand in China.
I don’t know if the industry is mature enough for that. There are different voltages, max power outputs and sizes. A set a size and voltage defines nearly everything.
Standard specs are great for something that is replaced frequently (alkaline batteries). It’s less needed for things that are replaced rarely.
I know a guy who started a company to do exactly this (in Europe only for now).
So the battery swap idea is out there, and being acted upon.