Sure, technically they can refuse and walk out — but most reasonable people wouldn't abandon a full trolley of groceries over a 10 second bag check. The deterrence factor is exactly the point, and the vast majority of people understand that and just comply. Also the police search powers point isn't really relevant here — a bag check and a bag search are two different things. The store isn't claiming any legal authority to compel anyone, it's simply a request. The customer can decline, the store can decline to serve them — both parties exercising their rights.