I know of a few teams that do this, but it is rare. DD was offered a spot on an 18u team last year that worked this way. For DD, it was a deal breaker. She likes playing the field and absolutely loves hitting. Personal preference I suppose...
When my DD played she only pitched in 16U, 18U, HS and college. She and I never had a problem with that. She played on very high level teams. There were always better hitters on the team. She was a the #1 pitcher and did her job well. She got the most innings and was handed the ball for all the big games. She did what was best for the teams.
In college the coach would use her to send a message to the other players who weren't getting the job done at the plate. She would bat my DD. If that happened the players knew they were on the coaches $hift list. In 4 years of college I think my DD had 8 official at bats. She managed 1 hit and a BB.