No doubt that greens fees are certainly a barrier. The muni near me [1] (bordering the Boston city limit) charges $10 for a junior, which equates to about $2 an hour given the pace of play on a busy golf course. While I understand that is still not free, it is an very low barrier to entry.
Old clubs are very easy to come by (relatives, craisglist, loaners). The main thing that I feel is being overlooked on this thread is that balls can be had for free, given the child puts a small amount of time in to look for them. Walk along the tree line of any fairway in the world and it will not be long before you've found enough balls to fill your front pockets.