I think some courses could possibly have stayed open to members, if their booking system could have been managed by someone working alone, or from home, and so none of the course staff were at increased risk. Nearly every golf course seemed to have system in place to handle this in March, until it was just pulled altogether for the lock-down. No need for any cash transactions, pro shops and I can't recall anyone I've ever played with going back to the club house for a slash during a round for that matter. They effectively could have just left the players to it, and said "you're getting no support other than a tee time", and I'm sure golfers would have been made up. Players of other sports would have gone bananas though.
Even as a golfer, I'm still not convinced this would have been a good idea though, not because it wouldn't have been safe, more because a lot of people are tossers (even more so golfers), and if you give them an inch they will take a mile. But if these people were not playing golf, they would still just be going for a paper every day, or to the supermarket 5 times a week, they would still find a way to be tossers.
There is another line of thinking though, if golf hadn't been banned it could have saved a few potential divorces I reckon. Nearly every older bloke I've played with whinges about his missus or wife, no end. There's going to be tons of couples splitting up when this is done, where it's not been practical to split up during lock down. Playing golf is the only way to get away for a lot of people.