In piano, we know that this is also the point where the easy progress ends and it starts to take serious work to get better.
What is the point of competition? Especially at this age? There is the standard answers of the discipline of following instructions, of being able to see what it looks like to be good. It is an opportunity to socialize with kids who are doing the same things you are and that you will grow up with through the years.
The other thing that is starting is the concept of working up to something big. In TKD, we spent three weeks of both some individual classes and more intense time with my son in preparing for the tournament. Similarly for piano, the teachers are telling the kids that the competition is coming and they have to be more serious. And the kids pick up on the fact that the adults are being more serious. Also we spend time focusing on smaller things than normal.
Is it worth it? Sometimes, the attention to detail taxes the attention span at this point. For TKD, we can go through the whole thing, but we can only improve a limited number of points of improvement in a session. I suspect that piano is much the same. The benefits is the idea that the details matter, and that you are preparing for more than doing as well as the friends you see in class every day or week, but you are up against a standard that you have not seen. And then having to deal with the stress of the event itself where a very specific performance matters with no redo. And they should be very aware of the true quality of that one performance. The ability to handle yourself under the attention of a crowd is invaluable, regardless of the quality of the performance.