I'm sorry but it really wasn't obvious for me. So like an online shop for groceries but they don't deliver it to your home but at this shared storage location?

Doesn't realy change the second part of my answer though. People could already keep some stock at home right now but most just don't. I don't see how such a shared storage would change that.

Also stock up for a few months is what the government is for at least where I live. [0] Personel emergency supplies are only for the time till the government can start distributing their own stocks.

[0]: https://www.bwl.admin.ch/en/we-advise-emergency-supplies