There are many benefits to adding a competitive component to your tennis training regimen. The most beneficial aspect of competitive tennis is the instant feedback that you or a coach can develop from observing your match play. You and your coach will be able to make adjustments that can help improve your game almost immediately.
Another great aspect of competitive play is gaining exposure to the many different playing styles that exist in tennis. Some players may be powerful baseliners who choose not to approach the net. Some other players may use the "pusher" tactic, which allows them to play extremely efficient defense and essentially wait for you to miss your shot. Once a player gains experience against these different styles they can learn how to counteract them. In some instances you may even decide to adopt one of those styles. For example, if you are at 15-15 in a service game you may decide to use the "serve and volley" tactic. Doing so may throw your opponent off guard and give you an easy attempt at gaining a point.
There is no doubt that competitive play can enhance anyone's tennis game. However it is very important to train your mental game as well as your technical game. A nice exercise to keep your mind focused throughout a match is to follow the "five second rule". The "five second rule" allows a player five seconds to spend thinking about the previous point. Once those five seconds pass your entire focus is turned towards the next point. As tennis players there is nothing we can do to change what happened in the past. We can only look forward and try to capitalize on the present.