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Please Don’t Make Me Download Another App | Our phones are being overrun
(www.theatlantic.com)
This is a most excellent place for technology news and articles.
Might vary by locale? Around here (South US) it seems like every single store has their own rewards/discount/whatever system that requires your phone number but it's not necessary for the transaction... It's just an extra info grab.
Sometimes the user facing POS/credit card reader will let you handle it (enter/skip) but many places rely on the salesperson to ask and then enter it or skip.
But, I also don't get around much so my experience is limited.