Niall, I assumed it was about U.S. courses as there are far too many public courses on "the other side of the pond" that were public courses going back many scores of years before the first one on this side.
As for SFGC, it was founded by 4 gentleman from Scotland who came over and settled in San Francisco. They were principals of Balfour, Guthrie & Company, an affiliate of Balfour, Williamson & Company, Liverpool. When they held the ffirst club championship, the winner was awarded the Liverpool Medal. With that background, they certainly had no problem sharing the golf course they were allowed to build with the public.
As for the "pitfalls of playing on public land," it was the rare golf club in the U. S. that didn't build golf courses on land owned by others. Often it would be on farm land as growing of grass was easy and leasing substantial acreage to build a course on was as well. The problems in almost every case was that the property owner was always raising the lease rate a cosniderable amount when the lease was up. It became the norm to lease and then buy the land leased or buy the land and build as the elase was running out.
It was a bit different for SFGC at Presidio. They were forced out for political reasons. The head of the base, Brigadier General Arthur MacArthur (father of Douglas MacArthur) was not well thought of by the Secretary of War (today known as the Secretary of Defense) William Howard Taft, while a number of members of SFGC were friends of his. Taft would kept MacArthur from going any further in rank and so MacArthur got back at him the only way he could, by forcing his friends to find another place to play their silly game. And so, in 1904, he chose the Presidio to host the largest peacetime war games in the history of the country (up until that time). He ordered that the land on which the folf course was built be used first by the cavalry, then by the artillery and finally by having, as was reported in the March 1st issue of the San FRancisco Chronicle, "the Colored Cavalrymen Reproduce Battle of San Juan on Small Scale."
When he handed the course back to the club it had been so badly damaged, it was nearly impossible to play on it, though the Scotsman and their fellow members gave it their best efforts to do so. They finally saw the light and leased land in Ingleside where they built a new golf course for the club.