The UK Border Force wasn't having any of it. I spent a night in an immigration detention facility (which is broadly speaking a prison) and was sent back on the next flight.
For context: The border force found a receipt for registration as an Irish citizen in my luggage, which they interpreted as a sign I never intended to return to the US [1] [2].
US immigration is at least as severe and our immigration prisons are probably not any fun.
Get a visa from the embassy if you are planning an usual trip even if you are not required to get one, because neither the US or the UK is required to let anyone in.
[1] The irony that Irish citizens are entitled to live anywhere in the European Union was not lost on anyone during these proceedings.
[2] But they also interpreted a card from my aunt that said "have fun on your trip" as a sign that I intended to abandon my life in the US. They are really imaginative people.