I think most college coaches would love to have a roster full of 2-way guys. More bang for your scholarship buck, more options, and if a kid gets hurt or fails in one role, the team might still get production out of him in the other.
But the reality is, it's hard enough to get onto a college roster in one role. While there are definitely guys who can handle multiple roles, they are rare beasts. The higher the level of baseball, the harder it becomes to be both.
That's especially so given that the weight lifting regimes are markedly different for pitchers vs. hitters. A guy who bulks up his upper body for hitting power may put himself at risk of a labrum tear if he also pitches. Conversely, a guy following the pitching regimen might be diminished in his development of power, which gets to be a big deal when the kid who was a stud hitter in HS finds that his 380' fly ball to CF is no longer a HR, but rather, the proverbial "can of corn."
As for high school ball: I don't know of any HS team that's as strong as a college team, plus the rosters are typically only half the size (roughly 17-18 players vs. 35). That means you don't have to be quite as far up the ladder to play in both roles.
But the idea that a HS coach would play someone both ways just to let them have fun? I don't know any HS coach who feels like he's got a rec league team on his hands. Usually, HS coaches fall into one of two camps: The guys who play the best players period, and the guys who modify that to give seniors an edge in playing time. I think if you go into HS ball thinking, this is just for funsies, let my kid play -- you're going to find yourself quite disappointed, and maybe land in hot water if you let those feelings come out of your mouth.