A company called "Better Place" had this thought and was working on something in the early 2000s, but didn't gain any traction and eventually went under. They were working with a car company (Renault I think?) to make low cost electric vehicles that were everything but the batter, and the battery module was a modular component that could be removed and swapped easily. The idea was that people could get into an EV cheap, and the company would own and manage the battery hardware. Think a subscription kind of service for the batteries. You could charge up normally, or drive into a setup similar to a small automated car wash, where a robot would drop the battery from below the car and swap in a fresh one - 5 minutes to a full charge, back on the road. It eliminated the headaches of consumers dealing with aging batteries, keeping up with new battery tech, etc. Clever idea, probably a bit ahead of its time, they even did pilot programs in a few places.
The hot swap service was the part that was most interesting to me. Something that many existing fuel stations could adopt to create the infrastructure to handle supplying refreshed batteries, spreading a network throughout areas with existing gasoline stations. Too bad it failed to coalesce into something viable.
The problem that I see with this model is "value". A battery is basically a car part, opposed to "fuel" (a battery would compare to a gas tank, and electricity to gas). That means that you could potentially have a gray market for them (not sure how many people buy gas outside gas stations).
With that in mind, let's assume you'll have a "changing station" that will service 100 cars every 4h, which is the time that will take you to service each battery. That would mean that your station would have at least 100 batteries lying around at any given time (and also overnight). Let's say that each battery costs ~$10k, that's $1M worth of batteries lying around with minimum security. Keep in mind that we're talking 25 cars/h, or 1 car every 2 minutes or so, that's not a lot; real numbers should be higher, unless you manage to lower the service time, which I made up since I have no idea how much time would it take to service a battery in this scheme. You could also do a lot "tricks" with the "subscription" method, like returning a dummy battery in exchange for a "fresh" one, which would yield a ~$10k profit with little effort and exposure. The bottom line is very simple: car batteries are too valuable to be moving them around so freely, they ARE the EV, for not so overprices EVs, that is.