Some additional bits of information on the subject:
Why is 2 /32nds considered Worn out? I don’t know. It predates my involvement. I just know that when the laws were first put into effect on tires (about 1968), they included a requirement for a wear indicator at 2/32nds for all street tires sold in the US.
Is it a law that tires have to be removed at 2/32nds? In most states, yes, but there are some that have no regulation, and some that have exceptions to 2/32nds. There is no Federal law on the subject.
There is a push to move from 2/32nds to 4/32nds due to safety concerns. The problem is that while tires have more wet and snow traction at 4/32nds, the point at which traction becomes dangerous is relatively arbitrary. The traction curve is smooth with no inflection points or discontinuities.
When the Rubber Manufacturers Association was updating their pamphlet on passenger tire usage https://rma.org/product/care-and-service-passenger-and-light-truck-tires, they wanted to include a statement about how to handle which end of the vehicle new tires should go on - and in particular, at what point did it make a difference in tread depth. Michelin did some testing and came back that they could not detect a difference at 1/32nd, but could at 2 /32nds - just like you’d expect: Small differences don’t matter, but large ones do.