What would you think about scalar-typing? To keep it simpler you could have half, normal, and double value typings. STAB, weaknesses and resistances just get multiplied by .5 or 2. Girafarig could be normal & half-psychic, golem could be double-rock, maybe something like bibarel could be strictly half-water.
My worry is that it sort of… makes the game more complicated without adding any actual strategic depth. You’re still multiplying together a bunch of factors to figure out whether you can KO a given Pokémon with a given attack in one shot, or two, or three; there are still going to be some Pokémon that survive particular super-effective attacks and others that don’t. The decision-making processes, both in team building and during battles, are going to be the same; there’s just more variables to keep track of. I’m not sure there’s any compelling reason for it either; I don’t think there are any Pokémon that really need half- or double-strength types to properly express their identity. Also, double STAB would be crazy powerful and the idea makes me nervous. Pokémon already has some pretty big damage multipliers and I don’t think we need bigger ones.
P.S. Merry Christmas to readers who celebrate it, and happy solstice to those who don’t. I’m just sitting here in my made-up paradise country enjoying the summer sun and the freedom to gather in groups with people outside my household, so… uh… don’t worry about me, and stay safe, everyone – especially those in the US and UK.