The zuchetto has gone the way, perhaps not as thoroughly, but certainly in the direction of, high button shoes.
Out of the approximately 17,000 priests we have in the US, I would be surprised if 1% use it. Somewhat similarly is the use of the cassock. I have seen priests wear one, but honestly, I couldn’t say how long ago. I suspect that there may be some who wear it on the East Coast, as the East Coast in general is more formal than the West Coast. But, short of an order or a priestly fraternity, it has fallen from use. Which is not the same thing as “not ever used at all”, but rather, rare.
Likewise, the biretta, at least out here, is noted by its absence; I have not seen one since my pastor, prior to Vatican 2, wore one.
My recollection is that he had that perched on his head during part of the Mass; so perhaps the zuchetto likewise was regulated during the Mass - not forbidden, but worn only during part of the Mass. and perhaps that is a matter for the EF, and not the OF, but I have no inclination to research the matter.
And then there is the flat brimmed, round crown hat I associate with Italy.