Based on the downvote and your reaction, I assume I misread something. We're talking about why Americans sometimes prefer paying with cash over credit card, no?
I'm the immigrant in question. I pay with card for literally everything online and offline, except two things - my haircuts and my wife's nails. Both of which accept credit cards. I go out of my way to withdraw cash (10 minute drive) just for these two things. Both the barber and the beautician appreciate it, for obvious reasons. My cousin with housecleaning business also gets paid mostly in cash, also for obvious reasons. It's just a thing we do. I don't know if natural born citizens do it too or not. Personally haven't seen it.
And you wouldn't see it from the POV of a natural citizen, not being one, but I assure you it has nothing to do with immigration. Cash is one of the few ways the "little guy" can sneak things past the IRS.
If there's no electronic record, then there's nothing for tax authorities to compare your declared revenue to. If you say you earned only $1000, then for all intensive porpoises, you earned only $1000 and that's the end of it.