For Monster Taming franchises, the big ones that come to mind that are currently on the Switch are Digimon, Yokai Watch, and Monster Rancher if you include ports. There's a few more if you include spinoffs like Monster Hunter Stories, but those three are the ones that mainly dabble in the Monster Taming genre alongside Pokemon. I could see Digimon as it's successful in its own sphere, and while Yokai Watch is struggling, there is no denying the influence it had considering it contested Pokemon for a time in Japan so if it can get its footing again I think it could have a chance as well.
As for Fossil Fighters, I would like to see some representation for that one. I doubt it'd be a playable character since its last game was on the 3DS eight years ago, but something like the aforementioned T-Rex would be fun in some capacity.