I'm not going to weigh in on the main gender/stereotype discussion here (though I don't think there's an issue really) but I will briefly share some thoughts on the whole HM and NPC's using pokemon outside of battle thing.
In many games, Story, Gameplay and Logic are tied together in a way that means often for some areas to shine, others have to suffer, or one will struggle due to the restrictions of another. this is often especially prevalent with pokemon due to the fact that with the world built the way it is for its stories and gameplay, the inherrant logic of pokemon worlds is somewhat flawed and full of holes when you try to heavily investigate or try to flesh things out as much as a real world.
Some specific examples off the top of my head: (reborn and general)
Levels : this is a big one. very important for the core of pokemon gameplay, yet often causes logic to suffer greatly when it comes to relative power levels of people who you battle. Extensions of this are Level Caps and Gym Team Power, the former doesn't really make sense story or logic-wise, especially with opponents who obviously don't have any badges but match or exceed your level. simplest option here is making them fully non-canon but then they can never be mentioned in-game without breaking immersion. The latter is more just about logic/story inconsistancies regardless of which system you choose (most noticeable with julia, florina, shelly in reborn): if the leaders have separate gym and personal teams, why don't they use their strong pokemon in things like the raid on mosswater. if they just have one team, did we happen to catch them when they were weak and now that they've grown stronger, do new challengers then have to fight Julias lv60+ team to get their first badge? If someone has a consistantly working system for this, lemme know. (we won't go into gym leader rank/ordering based on this)
Out of Battle actions by NPCs: Reborn is more guilty of this than main games, but thats because it tells a more intricate story with more NPC interraction. This seems like logic suffering for the sake of story, and in the players case, due to the restrictions of gameplay. Example is coral pier, logic says that Amaria could've rescued oshawott in one of several ways with her pokemon, but instead we got nice interraction with Cain, Amaria and ourselves, Cain obtaining oshwott and a battle with Cain. We sacrificed logic for story. Things like saphira tearing down metal fences is a case of sacrificing logic for gameplay and story in that it gives proper progression of areas. One of the more glaring examples is that the player can't free themselves from the nuzleaf cage, which doesn't result in much story addition, and is more likely to be noticed by the player due to the wait time. this feels like a sacfice of logic for gameplay consistancy more than anything else, i.e "if we can cut/burn that, why cant we destroy XYZ?" Some of this comes down to suspension of disbelief and rule of cool, and usually if you aren't trying to be too critical and just immersing yourself in the story, its often not a big deal.
Not saying you can't be critical of this stuff, but it's important to understand that it's nigh impossible to avoid a lot of this with the world and gameplay we have and still have a good game.
That's all for now, not sure if I'll revisit this or not.