From my experience if you are trying to become a merchant mogul and make lots of caps you will be disappointed.
High tier stores require a lot of investment in caps and perk points for minimum benefits
First caps are generated in real playtime outside settlements so emulating sleepin beauty and sleeping for a century or become fossilized sitting on a chair wont help.
Caps generated from a store will be available in your workbench under the misc category. To make back your investment in a store will take dozens of hours of playtime.
Bethesda claimed that the best equipment will be sold in high tier store but if you are like me then you'll have your character decked in legendary gear before lvl 30 and I've yet to see legendary gear in a settlement store
So what are the benefits? For me the only benefit is to sell my loot quickly while I store my junk. The best shop for a ranged character is the weapon store as at tier 3 there is lot of ammo to be bought and it's the best source to pick up .44, .50 and shotgun shells for my character
If you can point out other benefits then please do