I love the fact that Friar's Head has no yardage on the card. When you play there, you just pick a set of tees and go, you don't even give it a second's thought after the first shot.
One of our "unusual" but entertaining owners sent us out to play Osprey South before opening without any yardage anywhere (not even on the card). We played by guaging our yardage. He also only gave us flags, because he couldn't find an alternative that morning. He wanted to open the course this way too, but changes his mind at the end.
I played the Creek Club without a scorecard and was left to guess a number of tee shots, particularly the threes, and found that to be fun.
I personally, perfer the game without all the yardage so that deception is an element that I get to use (as an architect). I find, when playing, I rarely get a distance wrong, and often use a knockdown or alternative approach to take out trouble. If I know the yardage, I try fly the ball in all the time. Yardage draws away some of the fun of the game, it makes it too precise, and less adventurous.