I flew into the US from Canada on Monday. Airport there does have the full body scanner, and the last few times I've flown I've been directed to the line for scanning or pat down (your choice).
There though they do have two lines where neither is necessary; just the X ray of carry-ons. A screener choses, and tells you which line you are designated to. So, there at least, they are doing "random selection", as opposed to everyone. It appears they are doing about a 60% random sampling.
If it speeds the process, and keeps flying safe, they can scan me as much as they like. And I'm not against the pat down, other than it slows the process.
A commentator/comedian, Andy Borowitz, wrote ... don't understand all those people complaining that airport security invades their privacy, but post the details of their entire private life on Facebook