I dont think I've ever seen it written or stated by anyone within the DA that they offer "the best way for a scholarship." If anything they will consistently state that they offer the best environment for development. And if the comparison is between the DA and any high school (minus IMG) that isn't even an argument.
You are correct that simply by having A cost, let alone an expensive cost, you limit the pool of players you will get. But with that said, there are many fully funded DA clubs, meaning it is free to play for them. Either way, while they may not get every single elite player in an area, it's very disingenuous to say they don't take the vast majority of them away.
You are also being disingenuous with the coaching and the training environment differences between DA and high school. For starters, you leave out the fact that while they are getting the "best" 15 kids in an area they are using those players to play against teams that are also the best 15 kids in an area. So it's not as if having top level talent automatically means they win everything (though I would also point to winning and losing being less of a factor in the DA environment as well). They go against mostly equal talent in competitions, making player talent less of a factor in results. In high school the level of competition for almost every team can vary drastically over the course of a season.
Ultimately, your last point on the coaching is an apples and oranges comparison. High school coaching is mainly about just as you said, building a program with the goal in mind to win as much as possible. While the DA is more about building a program with the goal in mind of developing the players within the program to their highest abilities as possible. Two very different missions involving very different coaches, trainers, competition, and training environments.
Sent from my SM-G965U using Tapatalk