You can only think of such a scenario right now with swappable batteries.
Indeed. Which brings up another problem in turn. If those batteries are really "dead forever" once their charge reaches 0% (or very close to that), you have the problem of being able to recharge the old ones in a given timeframe. If the problem is with the grid not being able to handle many people wanting to charge themselves, then you also have a problem to do the same with the old batteries.
So you would need to store them for some time, and spread out the charging process. Now if enough people use electric cars, that in turn means you have a huge amount of replaced batteries to charge. For now it may not matter much, and the replaceable battery concept will work, since there are only very few such cars in use. But if that number goes up a lot, you are basically back to square one.
After all, you _must_ recharge them to have enough full ones in stock. You may delay the time at which you recharge by having lots and lots of charged spare batteries in stock, but you still need to recharge the depleted ones.
Then, if you want to use a slow charging process (that is, recharging takes longer than discharging, on average), you need a lot of extra stock again, because all the cars deplete the batteries faster than you can recharge them anyways.
Then there is the problem that virtually all rechargeables suffer from self-discharge to some extent. So you can't just recharge them on put them on the shelf indefinitely. You have to constantly top-up the charged ones. Which in turn makes the stored energy more expensive the longer the battery sits there and is topped up.
The whole thing gets even more expensive if the electricity production itself is switched to renewables as well, to make it "completely green". Because then you need to use storage systems, which by themselves make the resulting energy output more expensive (buy energy to fill the storage, account for losses, reconvert it to electricity, again with losses, plus the cost of operating the storage).
So, unless we get a really dramatic improvement in battery life and quality, plus a big improvement in mileage for all-electric cars, the whole thing will be just something that is feasible for short distances/city-hopping.
Greetings,
Chris
ETA: Not to mention the problem of quality-control and -ensurance that comes with a swappable battery system. You have to trust the "gas" station that the batteries you get are OK, that they are cared for properly, etc. Unless you want to have them recharged at the manufacturers place to get that level of confidence. But then you need to move around a lot of those batteries, which are quite heavy too, causing lots of extra traffic.