Honestly, I've been considering just cancelling my Costco membership. Sam's Club let's you scan as you shop, check out on your phone, and walk out. If Costco let you do that, it would help cut down on this greatly.
Only let two phones be registered at a time and that's your ID. Or have different tiers for solo, duo, or family with different price tiers. If you get a new phone, you have to invalidate your old registration. Have TOTP or one-time QR codes generated in the app for when you check out in line or at the gas station. Let the old people still have cards, but you check their ID every time. If someone forgets their card, let them look it up by phone number and present an ID to prove they are that member. Could even give $10 off a membership for going digital or an extra 60 days of membership if you go all-digital to incentivize it. When someone goes digital, flag their card barcode as no longer active in the system if someone tries to use it.
If you go digital, you get to scan n go and walk right out. Someone scans a QR code of your receipt as you leave like they do at Sam's Club. Sam's Club even let's you scan a gas pump with your phone and it will already program in a credit card of your choice, tie that pump to your membership, and give you a digital receipt. Totally paperless and basically zero contact.