The purpose of this question is to highlight the importance of a course being a reasonable, enjoyable walk through the park.
Every golf course can be walked in theory, so an arbitrary line must be drawn between "walkable" and "unwalkable". Once again, I'll use Stone Eagle Golf Club as an example. I typically walk it once a year to prove I can do it. It has relatively short green to tee walks, but the terrain is steep, and requires a few walks through deep ravines. If I walk and play with purpose, it takes me three hours to play the course by myself. That gives me time to think about every shot, measure distances, and pull the flag out for putts. For the sake of argument, we will define Stone Eagle "unwalkable", as is any course that takes more than three hours to play alone (quickly).
Another good yardstick is The Walking Golfers Society "Walkability Ratings" chart. Anything that is rated RED is unwalkable. Rob Rigg's ratings aren't refined at this point, but they do a good job of identifying the unwalkable courses. Help him out if you have opinions.
http://thewalkinggolfer.com/twg_walkability_ratingsI shot my career lowest round at Stone Eagle on a day I walked the course with Peter Ferlicca six or eight years ago. It's a fantastic feeling to play golf when you're really sweating to get around the course. There's little or no tension to deal with, but you have to hit shots while breathing hard, a unique challenge. Last year, during my yearly walk, I also shot my best or second best round of the year.
What do you think is the greatest unwalkable golf course? For many players the question is moot, as they regularly play the game in golf carts. For a cart player, the transitions between holes, and the severity of the terrain, is less relevant to one's evaluation of enjoyment. However, I would still argue that no unwalkable course exists that earns a consensus rating of greater than 7 on the typical Doak scale.
Doak 7 - "An excellent course, worth checking out if you get anywhere within 100 miles. You can expect to find soundly designed, interesting holes, good course conditioning and a pretty setting, if not necessarily anything unique to the world of golf."
Doak 8 - "One of the very best courses in its region (although there are more 8s in some places and none in others), and worth a special trip to see. Could have some drawbacks, but these will clearly be spelled out, and it will make up for them with something really special in addition to the generally excellent layout."
In my opinion, all unwalkable designs should be downgraded at least one category. For the best of these designs, the limit so far is 7. If you disagree, please cite an unwalkable course where the quality of golf holes and general ambience deserve a rating higher than 7. Ultimately, the limiting factor may actually be quality of golf shots limited by severe terrain, rather than the fact the course is too hard to reasonably walk.