At the same time, though, the thought is "a criminal won't give out their business burner's cellphone number" to sign up for a card/unlock a case. There's still an additional level of self-selection required to be honest enough to want to acquire the loyalty card that a "dishonest" person does not want to spend time doing (they want to snatch and run).

Same reason Walmart gated the self-checkout Scan-and-Go-via-phone system behind a paid membership on Walmart+, criminal's not gonna burn fifty bucks to steal a couple times if they have to hand over anything vaguely close to PII, even if it's burner PII.