Babies Are No Good At Playing Fetch

It's a good idea, as long as they can quickly recharge batteries it should work pretty well aside from the occasional slow down from excessive demand.

good...

If they swap batteries as often as my kids do (I keep the recharger in my room), they will be scrambling to keep up!

There's logistical issues with swapping batteries. Older or improperly cared for batteries will hold less charge than newer batteries. You'd be in for an unfortunate shock if you took your brand new car with brand new battery pack, went to a swapping station and left with 5 year old battery pack.

You can deal with the economic portion of that somewhat by adding a battery wear and tear surcharge onto the swap cost, but it would have to be part of multi-station system in order to balance the wear on the communal battery packs evenly.

While convenient, I'm not sure it swapping is ultimately necessary. Newer vehicles can do quick charges to 80% capacity in less than 30 minutes. While not as quick as gas, newer models are looking at 300 mile ranges in theory, so 20-30 minutes every 4 hours on the freeway isn't horrible (probably better for your body too).

I lease welding tanks for $5 a month, and swapping them out sure beats waiting for them to be filled. The leasing company is responsible for tank maintenance, and I'm sure it would be the same for batteries.
The bottom line is that a battery swapping station couldn't send out bad batteries any more than a gas station could sell bad gas.

I agree with ernest. Most naysayers only think of, or are only willing to acknowledge, what can go wrong, not how to avoid those things. I'm starting to suspect nay-sayers have stock or some other financial interest in the status quo.