Monster Hunter feels like it got two major strikes against having a playable character. Monster Hunter has the most content of any third party added to Smash, but without a playable character for one. A Boss with his own section of World of Light that also doubles as an Assist Trophy with a Spirit and two music tracks with a 2 previous Mii Costumes that have a high chance of coming back eventually? That's a ton of content for a third party franchise that doesn't have a playable fighter.
Then Byleth casually came in and took the most obvious Monster Hunter gimmicks with weapon switching, right down to the fact that Byleth's relics are also made of bone like Monster Hunter weapons could easily be.
I usually don't like to fully rule series out like that, but Monster Hunter feels like one of the more definitive franchises that Sakurai has decided on having a different role than playable fighter. Not that I would mind a Monster Hunter, but I don't expect it.
I don't believe Monster Hunter will be playable either, but the 'Byleth stole their moveset' but has always been the weakest argument against it. MH doesn't have the whip sword that makes up the majority of Byleth's moveset, Byleth doesn't have the iconic Great Sword that would make up the Hunters, and the axes and (to a lesser extent) lances are used differently in both games with MH using them armor the transforming Charge Blade and Switch Axe while MH's Lance's are more used for slow, defensive and precise strikes. The only similarity they truly have is the bow, and even then it's not like they don't have a multitude of other weapons to use such as the Dual Blades, Gunlance, and Long Sword, while also having items like the Flash Bomb and Barrel Bombs.
If you think MH is unlikely due to the Rathalos, that's completely understandable. However, Byleth would never be an obstacle as the characters have many more differences then you're giving them credit for.
Edit: To give a better idea, here's her
showcase from MvCi. Note that the only real move she shares with Byleth is the Bow, otherwise her primary weapon was the Great Sword with the Dual Blades and items like the Barrel Bomb being supplements.