My Umpire chapter, like most I assume, assigns Freshman and JV games to our most junior umpires. It's always been a rule of thumb that your better and more experienced umpires get the Varsity games.
The only drawback to that is, that it is in the lower levels that all the situations that the rule book can throw at you show up. I do a varsity game and its like clockwork. Players run, catch hit, throw, appeal. I do a Freshman game and its like the circus came to town. Batting out of order, illegal subs, illegal bats, anything and everything. The players are inexperienced with Fed rules, the coaches are inexperienced with Fed rules. Throw in a few experiences with an Umpire like the one described above and you have quite an afternoon on your hands.
The one thing that constantly haunts a dedicated umpire is having to overcome our less than dedicated members.