In golf, you compete against the field. Since there are nearly twice as many people in the U.S. now than in the 1960s, it stands to reason that as an absolute number, there are roughly twice as many people playing golf, twice as many scratch golfers, twice as many professional level golfers, and as a result, the fields are much, much deeper than in the past. Consequently, the probability of any individual golfer winning a tournament goes down significantly with the depth of the field. This is purely a mathematical argument and doesn't even include the leveling of playing fields due to technology. I also believe the numbers today are more than double because of more affluence and a greater number of golf courses.
One reason that it appeared there were more great players in the past is because less field depth meant that it was easier to win a tournament. You can also look at it like this (using extreme numbers for the sake of example), if there are 25-people in a field capable of winning a tournament, the odds of any one of them winning a tournament would be 25-1. If there are 100-people in a field capable of winning a tournament, the odds of any one of them winning a tournament would be 100-1, or in other words, any given player is four times less likely to win a tournament than with 25-winning quality players. Using these numbers, a 4-time major winner (in the 25 person example) and a 1-time major winner (in the 100 person example) would be roughly equivalent from a mathematical perspective.
For anyone who disputes the viability of these numbers, look at the depth on the Nationwide Tour, the depth on the mini-tours, and the number of former PGA Tour winners who fail to make it past the second stage of Q-School much less to the Finals.
