The evolution of what constitutes a major is an interesting topic and I have always felt that, among the four, the Masters is sort of an outlier. There is an inherent reason for the other 3 acquiring major status. The US Open is our national championship; the British Open is the oldest championship; and the PGA is the championship of the national trade group of pro golfers in America. These tournaments are controlled by the principal governing bodies in the game.
The Masters, on the other hand, is controlled by a private club and is totally independent of any governing body. It achieved major status by virtue of the Bob Jones connection; its place on the calendar; the course in its original form; and brilliant marketing, including renaming the event the Masters rather than the Augusta National Invitational, which doesn't sound much different from Bay Hill or Colonial Invitational.
The Masters, on the other hand, is a brand. The men who control the club are extremely conscious of the brand and go to great lengths to preserve it. The insistance on referring to the gallery as patrons; putting blue dye in the ponds; exercising dictatorial control over the broadcasts and shipping in all those flowering shrubs is all part of brand management.
I don't think there's any parallel where a private club controls one of the signature events of its sport. Wimbledon has been mentioned but I don't think it's the same.