I actually requested a card at Safeway (wanted for convenience, not privacy), but apparently they are not giving those out anymore. You have to give them your phone number or else accept the additional costs for your food and lack of benefits at the gas station.
The rewards card is a much better model in my opinion because while it gives them quite a bit of data, it does provide some anonymity. I'm sure it is possible to reconstruct from that data who I am (i.e. convert it into direct PII like name and address), but that at least takes a lot more effort and processing than if they have my phone number.
Most people are ok giving up SOME privacy for the sake of convenience/cost savings. I doubt most people are truly willing to give up all privacy for said benefits once they understand what they are actually giving up.
The typical model that I'm familiar with on those rewards cards is that they just ask for that same info for you to get the card in the first place, so it's of basically no benefit privacy-wise. I suppose this can differ from place to place, and you could always supply a different number or one not strongly linked to you, I guess.
Not at most places and often times that number will have a large reward points pool already built up because others are also using it to avoid giving out their number.
That at least takes extra processing and data sets. I think that does matter as far as privacy is concerned. We tend to think of privacy and security as all or nothing, but it really doesn't have to be that way and may be impossible to achieve if you go down that route.
The rewards card is a much better model in my opinion because while it gives them quite a bit of data, it does provide some anonymity. I'm sure it is possible to reconstruct from that data who I am (i.e. convert it into direct PII like name and address), but that at least takes a lot more effort and processing than if they have my phone number.
Most people are ok giving up SOME privacy for the sake of convenience/cost savings. I doubt most people are truly willing to give up all privacy for said benefits once they understand what they are actually giving up.