I routinely refuse to provide ID when asked by private businesses. About half the time they're OK with proceeding with whatever without it.
There are however many, many things that you are simply entirely barred from doing in the USA without showing ID. It's even worse in Europe.
Many music venues (the vast majority), all federally licensed firearms retailers, almost all hotels and modes of travel.
Perhaps you can live without music, air travel, hotels, and firearms, but I cannot.
I routinely refuse to provide ID when asked by private businesses. About half the time they're OK with proceeding with whatever without it.