I like to think of it as this: There is a base value that a typical golf course is worth given its location. Average course in Chicago: $8M, average course in Indianapolis: $3M. With a "typical golf course" being an decent track by a good regional designer and a standard, 7,000 SF clubhouse (for daily fee courses).
From there, there are a great number of factors that influence whether a particular course exceeds or is below that average value, the largest of which is location (freeway access, side of town, etc.) Other factors include the size and efficiency of the clubhouse, management, and architecture, which can be very important. Difficulty, maintenance cost, uniqueness, designer name, are all contributors to the revenue and expense. That determines the profit, which in turn determines the value.
What determines whether or not a course "fails" is your definition of failure. Most people generally consider bankrupcy or foreclosure a failure. But debt, cost, value, and purchase price are all independent of each other and you can have a course worth $20 million go bankrupt if it has $30 million in debt. Does that make it a failure, not really, it just means their loan is too big. On the other hand, if you spend $20 million to build the course, have no debt and it turns out to be worth $1 million, you aren't bankrupt, but I would call that a spectacular failure.
Long story short: architecture isn't the biggest determinant of financial success, but I would say it's up there.