If it really is only one effect per type I'm not a huge fan to be honest. I think it'd bring back a problem that was essentially gone since the physical/special split in gen 4, namely that being either physically or specially oriented would give a significant advantage or disadvantage depending on your type. For example, if you'd Dynamax a Tyranitar and it could use Max Darkness, that lowers special defence of the target. There's little use of that for Tyranitar, as Tyranitar usually attacks with physical moves. Tyranitar would also be able to use Max Rockfall, which sets up sandstorm when used, and Tyranitar also has little use of that seeing as it already sets up sandstorm with its ability.
Simply put, Dark types that are physically oriented like Absol, Weavile, Tyranitar, Bisharp, Mightyena, Scrafty, Incineroar, and so on would benefit far less from dynamaxing than Dark types that are specially oriented like Houndoom, Greninja, Darkrai, Hydreigon, or Yveltal.