They also weigh an absolute ton, so specialized lift equipment is needed; they take up space and will be very difficult to move around. So, are we expecting to stock a huge pile of batteries somewhere with an automatic loader/unloader that can handle multiple people at once with a quick turnover rate that can put away a 2000 pound battery? It's just too much infra, compared to a charging station...
And then there's the matter of the vehicle design; chassis rigidity is important and batteries, being a huge weight, need to be positioned properly with enough load bearing structure around them to support this. I'm imagining a hydraulic lift raising a 2000 pound battery up into my car; some massive brace needs to be attached below it to hold it up. Talk about difficult to get right; we've got harsh conditions like road salt and rust to deal with, and we have to make a fully automatable fastening device that can work at a random gas station with any brand of car... yikes.
You're actually much closer to the idea with the reduce-capacity idea. I had a Ford Focus Electric a while ago that had about 80km of range on a good day. This was more than enough for 90% of my driving; my old SUV handled the rest. Net carbon savings were huge; pity it was totaled in an accident or I'd have kept it going. Even at almost 10 years old it still kept a charge no problem and was a delight to drive compared to a normal Focus. My current EV has far more range but feels heavy and ponderous despite nearly 500 HP.
So not impossible, as long as the battery can handle the current. It's obvious that charging technology is not going to be the bottleneck.
(A real battery would probably have a charging curve that slows down towards the end, so more than 6C would be required in realistic conditions.)