It's true the pros workout. But the problem is the pros have spent significant on court time honing their strokes - lots more then average players are before they are even 15.
Once you have achieved excellent strokes and have great footwork there are gains to be made with fitness and athleticism. That's because the pros are evenly matched skill wise and fitness can seperate them.
I think young amateur players should concentrate on injury prevention with their workouts and just play alot of tennis.
Older players are going to have different priorities - with many athletes working out to maintain strength levels (and vanity) - and hoping to help their tennis some..
But the fastest way to get great at tennis is play alot of tennis under the watchful eye of other pros, IMHO. In short the higher your NTRP the more fitness is going to be a factor - unless you are grossly out of shape.