Quite a few of the courses in the Sandbelt [Melbourne] have three par-3 holes. My memory is a little foggy this week, but I think Kingston Heath and Commonwealth are two examples.
I have done a couple of routings over the years that had just three par-3's, but I've never had a client who wanted me to go that way. Average players look forward to the par-3's as their best chance to make a par or a birdie, and most of my clients, at least, skew toward average golfers instead of elite players.