The notion girls aren't allowed to battle is dumb considering literally 90 percent of Ash's opponents have all been girls
Visquez, Korrina, Iris, Bea, Marnie, Drasna and upcoming Cynthia and possibly Diantha
Heck when it comes to his main PWC battles, the only guy so far is Volkner, with Raihan, Lance and Leon coming up and possibly Steven
Just because a girl doesn't have the goal of battling right now doesn't mean they consider girls unable to battle or unable to be Pokemon trainers. It's just something they don't want to repeat with the female character and it's not coz they are 'sexist' but because they want to attempt a new storyline for their girl characters