Modern building standards make it extremely likely a fire cannot pass between units (you can never realistically entirely remove it - people occassionally do things like hang sheets off balconies or store tanks of fuel etc). This is before we talk about how many fires are put out by fire brigades before they've fully destroyed a single unit.

Honestly - the risk of a fire in your own apartment is drastically higher than the risk of it being engulfed in a fire caused outside of it.

Also the rental of storage space is booming. Pelican Storage seems to be the biggest operators in this area (at least in EU).