Any sensible proposal for electric systems for commercial aircraft is going to aim for batteries to be safely swappable in 10-15 minutes. (Though they can still make delays from unexpected diversions to airports without a stock of batteries worse)

The structural penalties for making "most of the weight of the aircraft" removable will probably lead to a plane that doesn't fly.

... for example, putting the batteries in the existing form-factor of removable cargo containers used in jumbo jets.

Hmmm... I wonder. Let's say they design the aircraft around an existing battery (size/weight). If later technology allows for a lighter battery, would they they have to add the weight back in order to keep the cg correct?

And then charge overnight and be used as energy storage for the time they're not in use. As flight times are very predictable, they should be a good use case for battery storage.

They say they plan to package batteries are packaged as standard freight containers.

Since current turnarounds include freight container swaps, I don't see why a battery swap wouldn't fit in it.

Supercapacitors could solve that, but unfortunately they currently have much less density even than batteries. Apparently graphene supercaps may solve that, but not at the moment.

Tesla style battery swap perhaps?