I think it is sheer numbers who play and playing opportunities. Our basketball kids can play 15 hours every weekend in pick up games, then go shoot 1000 baskets on their own. When they show promise, they can join AAU and be tested by other highly skilled players every practice and game. Never going to duplicate that in tennis, so many less players, distance to cover.
But one big problem is in America we shy away from our kids hitting with each other!! I have had so many older girls who make excuses not to hit vs my girl. I found a guy from South Africa who volunteered to hit with her yesterday and they had a blast, he was a excellent player over there. But its almost impossible to find adults who will bother hitting with a kid.
TCF your second paragraph is what we went through for years , my advice is the ball machine make the setting to where she can get a rhythm , trust me focus on clean strokes and movement , I was doing a lot of hand feeding till he was 14 , wish I had bought a ball machine , we use one regularly now and now he is a top player every one wants to hit "kinda irritates me " but its all good .