I would guess that most of the U.S. Opens before 1920 were played on courses that had no fairway irrigation, but almost none since then.
The R & A required all Open rota courses to put in at least one row of fairway irrigation after the 1962 Open at Troon, which was heavily criticized because the surface was so bouncy. When I lived there in the 1980's, most of the greenskeepers made it a point never to use the fairway system, and only watered by hand when they felt it was necessary. So, they have it, but most of them don't use it much.