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 does also help 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.

I understand that each state makes adjustments to this which may grant more or less powers, but here’s a Wikipedia on the overall concept:

https://en.m.wikipedia.org/wiki/Shopkeeper's_privilege

So for example during the aforementioned security theater at the doors, someone who is legally a representative of the company ownership(generally the managers making salaries are bonded to this) is doing their best to catch someone in the act of stealing, putting something in a coat, loading a cart and bypassing the register, etc, and this gives them grounds for some mild detainment. This apparently covers them stopping you at the door or firmly requesting you join them in their office to clear things up(and wait for the real authorities), and means no one questions if they grab the cart which is company property and doesn’t let you leave with it.

I once sat and chatted with one of these guys waiting for a bad downpour to stop. Being stopped sucks, I know, but here’s some insider information:

They are stopping you for appearances. They absolutely are skimming your receipt, they really don’t care about you personally. It’s all circus.

If they are looking, they are looking for the big loss items. That TV that gets rung up in the back, was it actually rung up? The water case under the cart coming from self checkout? Another big loser for the company. Coming with a tote or loaded cart from the wrong direction is a little obvious to everyone.

Every other stop is for show. To remind the tote runner they are watching. To make the TV thief skittish. It’s all about appearances and breaking down resolve. The door guys can’t stop you, but they can make you afraid that they are vigilant and someone who can is waiting(and the salarymen can, shopkeeper’s privilege apparently in the US). It does work, loaded carts abandoned near the doors apparently testify to the effectiveness.

Some door hosts get by with being passive, they are supposed to be pretty chill and friendly, and dial up the theatrics when someone is reported to be suspicious or when a “frequent flyer” walks in. But that just makes it seem discriminatory and unbalanced so apparently some managers want the theatrics 24/7 to avoid the complaints of unfair treatment.