The only issue is people being against it politically/socially.
The chargers can either do it by themselves (adjust load to match hookup to grid) or the power company can manage it. Usually it's a lot easier just to manage it locally.
You're thinking of the fridge-sized units with the wrist thick black CCS cable. Yes, those need very specific grid hookups.
I'm thinking of, you know, a household plug. The kind an American would plug in their dryer to. You don't need a separate substation to run a dryer, right? Even if an apartment building has 20 of them.
One of those can charge 100-150km of range to a car overnight easily, which is more than the average person drives every day. YMMV.
Oh yes, you do. If too many people run too many electrical appliances, the grid needs to be upgraded.