I reject your premise.
Successful tour pro architects include: Jack Nicklaus, Greg Norman, Arnold Palmer, Ben Crenshaw, Tiger, Jerry Pate, Graham Marsh, Tom Lehman, Tom Watson, Davis Love III, and others.
Other outstanding players turned successful architects include: Donald Ross, Old Tom, Pete and Alice Dye, Steve Smyers, Bill Diddel, William Langford, James Braid, and others.
Undecorated golfers who are successful architects include: Tom Doak, Seth Raynor, Bill Coore, and surely plenty of others... I can't guess the handicap of guys like Gil Hanse, Perry Maxwell, and others.
In a great big world, where only around 10% of golfers are better than a 10 handicap, it seems very clear that experience playing the game at a high level improves a person's likelihood of having a successful golf course design career. It's not essential, and it might be interesting to talk about the differences between courses designed by great players vs mediocre players. But I do not think the history of golf course architecture shows that elite players struggle to design great courses.