I don’t think you’re wrong to want to use another system to emulate MTG magic, and your reasoning is perfectly valid, but this bit... Isn’t really true. There are a lot of effects that show up in every color, yes, but there are also a lot of effects that don’t, direct damage and life gain among them. Blue and red don’t have life gain and white and blue don’t have direct damage, outside of a few much older cards that wouldn’t get printed under the current design paradigm. Counterspells basically only show up in blue with a few rare exceptions, likewise for unconditional creature destruction in black. Red and black can’t destroy enchantments, and black can’t destroy artifacts. There are a lot of restrictions around which colors can do what.
Obviously, as it’s a core mechanic of the game, though notably the colors do so at different densities - white gets the most creatures, followed by green (green gets the biggest creatures though), then black is the middle of the road, red gets the second-fewest, and blue gets the fewest.
Ironically, poison does actually show up in every color, via Infect. It was the signature mechanic of the New Phyrexians, which appeared in every color. Though I expect if the Phyrexians return, we probably won’t see Infect again because it was massively overpowered and generally not very well-received.