Not likely, but US border officials can pretty much exercise arbitrary power in deciding who gets in, and they can’t get in trouble for denying entry to a non-citizen Joe B. Nobody.

Not British, but two Irish acquaintances of mine were rounded up and deported from the US in the early 2010s. I don't see a problem, they broke the law in illegally moving there. Such practices were common among Irish up until the 2000s. Doesn't happen so much anymore, but then again it is near impossible to legally emigrate there if you're from Ireland.

Yes, they do have issues with this. Whether UK or any other nationality. Funnily, I have a colleague who overstayed his entry visa by exiting a day late and frequently gets stopped and questioned when he goes back, which he does often as he had since married an American and probably entitled to US and UK passports by now!

Getting a green card would presumably reduce his border hassles. On the flip side it would require him to file US taxes as long as he retains it no matter where he lives.

In my case even with that I got hassled every time - multi hour delays on every arrival because of something screwed up in their records of me. Eventually I went so far as to get citizenship because of the hassle. That requires me to file US taxes for the rest of my life even if I choose to permanently reside outside the US.

It happens.

https://www.dailymail.co.uk/news/article-6665949/The-birth-c...

A problem as in "people of that nationality causing problems" probably not as much.

A problem as in "it is against our current immigration rules" technically it is correct. Numerically it's probably around < 1% possibly around 0.1%