Doubling is key to reaching the top levels of competitive running. You will be hard pressed to find any distance runner in the top 20 in the US or top 50 in the world that do not exercise twice per day on average (more than 10.5 workouts per week during normal training). I feel that doubles are a privilege. They are a reward for reaching a level of fitness where more improvement requires more than one workout or run per day.
Unfortunately, I had a bad experience with doubles in high school. We were running at 6AM four times a week before school and every weekday after school. I burnt out that season. I set a personal record by seven seconds in the 5k that season and our school had the best finish ever, 1st for the women and 7th for the men. I also did yoga 10-30 minutes almost every night that season. We were only doing 3 miles in the morning and as low as a mile in the afternoon but often 3-6 miles.
I feel that the benefit of the "easy" run in a double is about half that of the main training run. So a 10mi morning and 10mi evening run is equal to a single 15mi run. I feel that until you are doing 10 miles per day it is not worth your time to double, although, for injury prone people or short distance specialists (800, 1500, mile) the situation may be different. For distance runners improving your aerobic endurance is accomplished on pleasantly hard runs and your lipid consumption rate is improved on longer runs after the first hour of running is complete. So to have success at the half marathon and longer it is imperative to run for more than an hour.
There is also the factor that every run typically involves changing twice, showering and some stretching and eating component. Those things also take time. Also, any run that takes away from the main workout of the day must have a purpose. That is why most professional runners do their quality in the morning so that their recovery run in the afternoon will suffer instead of their quality. Another thing that professional runners do that normal people do not, is recover well. They sleep more and spend more time resting. As a student I had trouble waking up at 6AM to run, going to school, running at 3PM and then doing much at all in the evening. As I become older it has grown easier, but then again I never have homework now.
So those are my thoughts. Until you are running around 10 miles per day you probably do not need to double. Yet if you want to reach the top, you will almost certainly need to double.