Of all the posts already on this thread, I like Rich's and Charlie Bell's best.
There are so many factors and conditions of play that precede the event of hitting a ball off the tee, that any hole could be anything from mindless hit it and find it, to serious thought or strategy.
Width to my mind is one of the most important factors when employing strategy, when the situation calls for strategy, which would be when you are competing, mostly in matchplay, but also stroke play 'competition'. Or, if you went out on the course alone, with the mentality of competing or "playing the course". When you are going to 'employ strategic thinking' you then consider wind, firmness in the LZ, slope in the LZ, etc, along with near and far carries to avoid hazards, or favorable angles.
When you are going out to just bomb and gouge it, just wail away, and find it to hopefully hit it again, then strategy isn't important. When you do that, maybe your goal and strategy is just to have fun with friends, enjoy a walk with intermittent acts of violence towards a ball employing a stick to beat it to death, etc. And, that is fine, if that is what you are out for.
But, when you play a course you think is great, good, challenging, or when for whatever reason, your round means something to you, if you have the resources, and you have the choice of employing a course knowledgeable caddie; aren't you expecting a partnership to employ a version of strategy. Doesn't a good caddie who knows golf and the course, suggest options and what to try to do on many tees (if you ask him/her)?
Of course, like JR Potts mentions, you aren't 'that good' to pull off what your mind strategises to attempt. But, when you do see something from the tee, if the situation of what your opponent has done or is trending to do dictates how you should respond or challenge if playing first, then you are using strategy, and you are competing. I fall into the hit it an hope category 90% of the time. And, I fall into the mindless hit it and find it most of the time, because I'm usually playing just to wail away and have fun, hope to hit anywhere on a FW, and anywhere on a green, then deal with what I have left.
But, when playing a match, a friendly Nassau or a skins with pals, and trying to win something, how can you not strategise and try to hit some sort of shot pattern, to match the architecture out there that awaits your play of that hole?
When you add what I believe are the most crucial elements to the equation, firmness and wind, to a width factor, and strategically designed or routed hazards with slopes at FWs and around greens, how can you not have strategy? If you have lush soft and flat FWs, with no hazard to avoid, you might as well go to the driving range.