I offer up 40 years of my life as a counter example. Maybe it's a bit city thing, idk, but this is not the norm where I'm from. You get the bill, put your card in it, they take it and run it, bring it back, and you sign the receipt.
I’d hardly characterize it as “perfectly normal”, although it is definitely a frustrating issue that provokes a great deal of controversy domestically (and seems to induce strangely aggressive statements from a great many folks commenting from countries heavily reliant on American arms for protection from their regional neighbors).
I can understand it being hard to reckon with when one’s primary understanding of government stems from a familiarity with countries founded in accordance with the desires of a handful of pre-existing, regional groups (as opposed to a country founded with explicit mechanisms by which new groups can achieve representation).