Way back around Gen VII or so I had come up with a new type in the same vein as the then recent Fairy type as a thinking exercise called Monster-type, based on the fact that there's a Monster Egg Group the same way there was a Fairy Egg Group even before the Fairy-type. The same way Fairy type serves as a counter to Dragon, I imagine Monster would be a parallel to it. It could be composed of mostly Kaiju like Pokemon, who all share design similarities in the same vein as Dragons but don't really fall into a same type, like Aggron or Tyranitar, Avalugg perhaps, etc.
I didn't really think that much about its type advantages and disadvantages, but I guess it'd end up being very similar to Dragon type, with Monster type being strong against itself. The resistances and weaknesses could be based around typical Kaiju movies, or thinking about what the weaknesses of strong, big, lumbering monsters would be. It could also be a stand in for a Radiation type, similar to how Pokemon Uranium had the Nuclear type, since Kaiju and specially Godzilla tend to be associated with that stuff.
Speaking purely from a game balance perspective, I do agree the easier route is to just re balance the type chart somewhat. But it was a fun thought exercise to think about what could be a probable official new type, based on the existing stuff from the games.