On one hand, a local owner might be more invested and thus more likely to DO something if they catch a shop lifter, which might be a deterrent.
On the other hand, a semi-local, privately owned toy store (1313 Mockingbird Lane), who has one of the nicest guys you will meet running it, has to post video or pics of shoplifters every 2 or 3 weeks because some people care more about free stuff vs supporting local shops or a passionate store owner for a niche product. I can’t imagine some small convenience store encouraging any loyalty that would dissuade shoplifters.
It is a college town, so you do have a lot of younger, adults with poor impulse control and often not a lot of extra funds