I'd say this is a case by case decision, both for coaching staff and player. So very hard to make a blanket statement. So many variables, and perhaps most important is what does the player want to do?
Some travel/showcase managers will only take a guy as a PO because his glove and bat don't impress them as much as the player's pitching potential or ability. Some guys are clearly "tweeners" where they are great at 3rd base and have a power bat and they can throw strikes but everyone knows they will NOT be pitchers at the next level, yet they do pitch often as a 16, 17, and 18 yo and are leaned on sometimes more than guys who are only POs. Like I said, very hard to generalize. Case by case basis.
Personally my son made the choice to focus on pitching only, and he needs to, as he has a lot of work to do. To taken BP and taking ground balls on top of working on pitching is too much for my player, and he made the very hard decision to forego being a 2-way guy. Has decided to focus the spare time when not working on pitching, to focus on basketball instead.
Very personal and difficult decision and process to navigate. Son does play both ways on HS team as they are very thin on talent and bodies. But for showcase, just PO.