could a charging site have a buffer of fast charging batteries?

Yes, but have you ever seen 8 queues of cars, about 8-10 cars in each, at Sams Club or Costco buying gas? You'd need a awful lot of battery buffer to keep up with that kind of demand. At some point you'd deplete the batteries and be stuck with charging at whatever rate the grid connection could deliver.

First, that exact situation simply doesn't have an equivalent in the EV world. Quite a lot of people should be able to charge elsewhere (at home, at work, on the street).

Second, wow, I live in Europe and I have never seen 64+ cars queueing at a single station. If I saw 15, I'd be wondering what the hell happened.

Lots of people (apartment dwellers) cannot charge at home. Charging at work or on the street is still a very uncommon option here (USA).

I’m an apartment dwelling EV owner, so I’m well aware of that, but even here, where high density housing is pretty common, at least 50% people could theoretically charge at home with no or minimal adjustments. And on top of that, workplace and street charging should follow EV adoption, it’s not like either EVs or the infrastructure are going to appear overnight.

With EVs, most of your charging should be done at home, with fast charging mostly just existing for trips.

I know not everyone can charge at home (especially if you live in an apartment), but the solution to that is pretty straightforward and a lot more convenient compared with trying to scale up fast charging to match petrol stations.