Let me preface the following by saying I haven't spent the time doing a detailed search, so if I'm wrong I hope someone will fix me...
I don't think the word "fairway" is in the rules of golf. A decision maybe, but I don't think it's part of the rules.
The word "should" is a strong word in the rules. I think if something is started with a "should", and you don't do said thing, you are in violation of a rule.
Hitting a fairway in regulation is a sometimes easier way to get to the green. Sometimes, but not always.
Hitting a fairway in regulation sometimes will provide you with the best lie/stance for the next shot. Sometimes, but not always.
Hitting a fairway in regulation is sometimes the goal off the tee. Sometimes, but not always.
Why should you/I/they try to do something 100% of the time if it doesn't provide the best potential benefit to your/mine/their score 100% of the time? I try to hit the fairway when it's convenient with what I'm trying to do on that particular hole, not because I'm just standing on the tee. That's the style I enjoy.