Look at sports where size isn't the goal of athletes - track sprinters, guards in basketball, etc... These guys aren't generally very big because they want to be quick. While football players lift for both hypertrophy and strength (because good football players need to be big AND strong), there is little reason for a sprinter or guard to be "big."
That being said, do these people look "big" on tv? Of course they do. Most of these guys have ridiculous body fat %s and still do have pretty big muscles. The amount of weight that these guys can lift though for the size of their body is unreal. If you train for strength (low reps) as opposed to muscle size, you are better off in many sports.
Not true at all. Fast and big are not related in the way you are supposing. Actually, with increasing size (at equal body fat percentages), more muscular athletes will be faster (up to a point). Speed and explosive power output from the lower body increases with strength because
speed is a function of strength.
There is Russian data that collected information on the vertical jump heights of olympic weightlifters. They found that the 90kg weight class had the highest vertical jump, not the lighter guys or the super heavyweights. This is due to a variety of factors, but these athletes are leaner than the super heavyweights, stronger than the lighter weight classes, and use fairly heavy loads in their training.
Look at the sport where being bigger hurts you: Gymnastics. In the men, there is a certain level of muscularity involved, despite not eating or training directly for it. Look at high level rings specialists, they are very muscular, and it is required for their performance.
Hypertrophy is absolutely required for higher level athletic performance. Granted, you don't have to be as big as a competitive bodybuilder, but you definitely have to be more muscular than a 12 year old stamp collector.
I suggest that you read this article by Kelly Baggett that discuses the idea of "nonfunctional hypertrophy" :
http://www.higher-faster-sports.com/nonfunctionalmyth.html