It's amazing to me how normal it is for even a seasoned golfer to have no clue how to read a green. A friend of mine is a 6-ish handicap with a really smooth, effortless and powerful swing. But he regularly has no idea at all which direction a putt will break.
I don't know how you learn to do that. I've always been able to read greens pretty well and the slopes have always seemed obvious to me without plumb-bobbing or aimpointing or whatever. But man, it's hard to understand and appreciate architecture if you can't read a slope.
I liked David's answer in the first reply. Even my mother, whose handicap probably never would have been below 30 had she kept one, has figured out how to move the ball both directions at a cursory enough level to enable an occasional great recovery shot. There's a difference between knowing enough to give yourself a chance when absolutely needed vs. trying to hit exactly the shot called for in every situation. Tiger's ability to do the latter is indeed spectacular, but as Ben notes above, it's a losing strategy for the huge majority of us. But I think it's hard to understand how architecture permits recovery options if you have no hope at all of hitting a recovery shot that looks different from your stock flight.
But I also like Joe's answer above - that having a lot of shots at your disposal might make architecture less relevant for you. And there's an idea on a similar note that I wrestle with a lot. As someone who at least pays a little bit of attention to architecture, I can generally grasp how a hole's layout is intended to challenge and reward a player. I can look at a hole with a bunker that cuts into Position A off the tee, and understand that the hole's strategy revolves around rewarding the player who drives it close to the bunker with a better approach angle than the guy who bails out away from it. But that DOESN'T necessarily mean that I should be trying to get close to the bunker off the tee. The right play for me if I'm trying to score is often to give it some respect, even if I'm making my approach angle a little less desirable, or adding 10 yards to my next shot, or whatever. Being able to say "That's a strategically placed bunker" requires a certain degree of architectural knowledge. But saying "I'm going to avoid it because I don't have a shot that I can trust to skirt it while staying out of it, and I'm better off taking my chances from Position B" is the difference between understanding something at a knowledge/conceptual level vs at an evaluative level. The latter requires greater understanding.
Maybe the answer boils down to something like: It doesn't matter how many shots you have, but rather, how well you understand the shots that a given hole's architecture will accommodate, and your ability to execute each of them.