I think the serve gets more and more important as you move up in NTRP. At the 3.0 level, service games get broken all the time and it has little to do with predicting who will win. A 3.0 player that can easily break an opponent's serve is little indicator of superiority on the court, since it has absolutely nothing to do and is completely unrelated to his or her ability to hold serve.
It's almost completely random if a 3.0 will hold serve or not. Unforced errors on both sides makes it nearly impossible to predict.
Now, at the 4.0 level, serve is significantly more important. A 3.5 player with excellent strokes, extremely low UEs, very good court placement, but has a horrible serve is going to get pummeled every time vs. a 4.0. It won't even be close. The 4.0 will likely break the 3.5 on 80% of the service games. And, the 4.0, who likely possesses a much better serve, will very rarely be broken.
The service game dictates how the point will go. A weak serve is no better or worse than a typical groundstroke, and therefore adds no momentum to either party. It's a nonentity and derives more points from simple UE's due to a lack of skills on the court.
A moderate serve is slightly harder to hit back than a typical ground stroke, and so therefore can be an effective weapon if placed correctly. It can dictate a little bit of momentum.
A very strong serve with good placement will almost always produce a non-groundstroke return: a block of some sort. It often is a high percentage shot which is in the middle of the court, plenty of clearance over the net, and a good amount of pace has been absorbed. This can be a very easy shot to "put away" by the serving player. If it isn't a winner outright, it can continue to keep the receiver on the defensive, never quite gaining ground. Thus, the serve is truly dictating the point and therefore has a high probability to result in a win.