I can't see why these places don't go the Sam's Club route, scan and go makes the dreaded run at least less appalling. Everything is on your phone, in fact you can even pay that way. Pick up bags or boxes on your way out the door. Have a designated entrance and exit with two people spot checking your order as you leave.
Give a discount to those who use the scan and go method, maybe a smaller one for the self checkout. Charge a premium for checks. Full price if you use the regular check out line. The public will go crazy, but most of them are there already.