Something that always didn't sit well with me when doing a singular composite is the uncertainty of whether the composite is being influenced by seasons which were more on the anomalous side. Now there is nothing you can really do about this, though I'm sure someone with an impeccable background in mathematics and programming could develop something.
For example, I've been working on this tornado project (which I started like 12-years ago) which I used for senior thesis, and then finally made some significant progress with during this past spring. But when calculating averages I was always worried about an average being skewed due to outliers. So let's say I wanted to calculate the spring tornado average for the whole U.S. Naturally you would just add up the number of spring tornadoes from 1950-present and divide by the number of years. But what I did was find outliers using statistics and removed any outlier years in the calculating of the average.
You have some Nina's that were quite cold and other's which were quite warm and at the end of the day how do these extremes influence the composite? It's with this that I think composites can be a bit misleading but that doesn't go to say there is value in them but I think the best value overall is when you're doing a composite of something that is extremely similar with little deviation (for example, creating a composite of the top 10 -NAO December's).