I'm far from an authority on the topic, but I'm fairly confident that the Monster Hunter situation is being misconstrued. As far as I'm aware,
this is the only word we have on the topic, and what it says is that when the MvC3 team approached the MonHun team with a proposal to add the Hunter as a playable character, they said that they did not like the idea of a single Hunter representing the series due to being a customizable character who lacks any certain identity. Monster Hunter has appeared in lots of crossover material since, including a card in UMvC3, several mobile crossovers like Street Fighter x All Capcom and Minna to Capcom All Stars, and the upcoming Worlds Unite, all of which use characters other than a Hunter. The MvC team didn't propose another Monster Hunter character as a follow up, so we really don't how they'd feel about adding a Felyne or a monster.
Very different than the Pokemon situation, which actually involves having to go through other companies due to Nintendo not holding exclusive rights.