You're not wrong that this fundamentally excludes those who don't have (powered-up) smartphones. But it's not like restaurants and bars had the luxury of thinking through and choosing to have these effective new smartphone requirements: they adapted to Covid for their survival, and the odd case who got unlucky with a dead phone is just collateral damage.
I'm in Canada, and we use QR codes, signed by the government, to show and validate status.
Mine is printed out, and in my pocket. No phone is required.
Thus, no one needs to avoid anything, phone or not.
Also, in your case, is this a federal system or a state by state one? If the latter, this sounds way worse than what NY is doing; with my CA vaccination I couldn't get in anywhere.
The QR code is provincial, but it only requires minor changes to have one provincial app, look at other validation sources.
I agree that sadly, restaurants may find some metrics too high/annoying to deal with, and opt for a lost sale.