Cash is fake, and checks are antiquated. If the money isn't worth the paper it's printed on in the first place, why even pretend? I'll stick with plastic for everything and not bother with the ruse at all. At least if my wallet gets lost or stolen I have some recourse to actually recover my "money," once cash is gone its gone.
I'm with eye95 on the rest. This isn't a govt issue, it's private entities looking out for their own (and your) interests, trying to prevent fraud by requiring ID or zip codes. I've only ever seen the zip code thing at gas pumps too, and there it functions similar to a PIN, to verify the card user. And I've never seen any place take any record of my ID when carded for a purchase, they're just looking to see that the names & faces match.
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