It doesn't effect the content of the chest. It just says who can access the chest. And yes you just have to walk up to the chest to look in it hit R. If your name or type is not the one on the tab page. Then access is rejected.
In order for the chest to not be destroyed to force access. The chest must be on the factions leader only buildright central part of the Home Base. The faction leader also adds his name to the chest. And sets the chests of the other members. This is only needed if you want an invulnerable chest.
As for immersion that is up to the individual players or factions. It should never be a forced uppon core part of Starmade.
RP is for hippies. The cargo update and personal inventory limit should be sun bombed. I simply want to consume every other player owned block on the server that is not in or on a Home Base.
I want my own Home Base stuff to be save. Without having to worry about who accesses my chests. Or the chests of my fellow faction members.
Adding a shops options tab solves that. The whole shop block tree should never ever be added to simple storage. Use a Shopblock for that.