If external cooling becomes the solution (which makes a lot of sense) then I think it's more likely that a car will be provided with a water supply during charging - a water connection near (but not too near!) the electric plug would let the charger pump water through the battery pack and suck a bunch of heat from the car, without a complex battery removal workflow, and without the heavy cooling mechanism having to drive around with the car.

If this were to happen (and I don't think it will), then you'd want that water connector to be part of the charging cable to avoid a two step hookup. That requires a new charging cable standard (which is why I don't think it'll happen).

Also, water kinda sucks to deal with for something like this. What if, for example, the water flowing in isn't pure? What if it's hard water? Your battery cooling tubes could need flushing and might start growing nasty fungus and such.

You could do a heat exchanger - no mixing of the water then but added complexity.