I think you have it right. Refusing the check is not alone sufficient grounds, and that is why if you (politely, no reason to be a jerk, they’re just cogs in a machine working for a pittance) refuse and walk away, they just turn to the next one.

It is, as many have concurred, for show. The idea that you may get asked, the anxiety that develops thinking you might get caught, deters all but the most hardened thieves. Same with exterior lights on a home; before cameras what good did a lightbulb do to stop a thief? Does a lightbulb injure or detain a thief? Call the cops for you? No. It upsets their resolve. The light may make them visible to a witness they aren’t aware of. And a witness might call the cops or hurt them. On to a darker house, then!

It’s not just about what’s legal for the store employees to do either. Were I a thief, I wouldn’t be worried the manager is going to ban me from the store, or the frail old lady they have at the door is a threat, I’d be more concerned what vigilante schmuck is going to “help” the store by taking matters into his own hands after he overhears me arguing with the greeter or manager. The store gives up after you leave the sidewalk, “hometown heroes” don’t.

Straight theft aside, I imagine it also helps them recover some losses from mistakes. Any time they catch somebody with legit missed items under the cart and guide them towards fixing it, loss averted. Start noticing it happens a lot from a particular cashier or self checkout supervisor and get them corrected, more losses averted. I imagine you’d need a fairly wide sample set to figure it out?

It’s not a…totally unfair concept in theory, but they really aught to find a way to make it feel less adversarial and it would be more tolerable.