9/10 and below, stealing bases is just part of the territory. At that age, I want my catchers working on fundies - blocking balls in the dirt particularly, to minimize extra bases as much as possible. But at that age, you're going to give up runs. I want my pitchers focused on throwing strikes and pitching to weak contact, my catchers catching/blocking pitches in the dirt, especially strike three, and most importantly, my defense making routine plays.
If you have catchers throwing behind runners or trying to throw out runners at that age, they can be little Yadiers out there, but that doesn't mean your fielder is going to catch the ball to make the play, or even be where he's supposed to be. That's why I want my guys focused on making the routine plays and limiting damage as much as possible - no walks, no errors, make the routine plays. It's a plus if I have a pitcher out there that does a good job of holding runners and we work on that too. A lot of kids will take off early on the bases and if you have a pitcher that can handle the situation without panicking (stepping off, running at the runner, putting a good throw on him), you can control the run game that way. A lot of times, I won't even hold on a base runner if I have a pitcher throwing strikes because it may be more valuable in that situation for them to be in good defensive position to make a play.
Once they get into 11/12 and up and the bases get more spaced out, you can start trying to control the run game a little more with your pitchers and catchers.
As far as offense, I want my kids aggressive on the bases, but the correct way. Certain situations are automatic steals at that age, no matter the speed of the baserunner. But I want all my kids getting good, aggressive leads, reading the pitcher and getting a good jump without going too early. I also don't just automatically send them first pitch depending on who the kid is. There may be benefits to not running them and just getting good aggressive secondary leads.
A lot of coaches run because they're trying to win tournaments. I want to teach my kids to do it the right way so they can develop into a kid more likely to make his high school team and get a shot to play at the next level.