I'm going to guess you live in or near San Francisco? Your view of golf is going to be skewed by that. While the Bay Area has extremely expensive and exclusive golf courses, it also uniquely has .. relatively.. affordable ones.
But consider even $20 to play a game involving a stick and ball is actually still quite expensive to a child, so that's still a really high barrier to entry for a lot of people.
Outside urban areas, there are still plenty of small local country clubs that provide "unlimited" golf facilities for Members & their kids for affordable rates. $100-300/month depending on area, quality, etc...
GolfNow and other TeeTime booking sites allow for discounted rounds in your area.
Its not as cheap as Tennis & Basketball, but its not a game for the Rich and Famous only.
But consider even $20 to play a game involving a stick and ball is actually still quite expensive to a child, so that's still a really high barrier to entry for a lot of people.