Part of my opinion here is based on memory only, but hear me out: The only games that used 1 coin switch per player were usually the 3 or 4 player games. That way, whatever slot was coined up, that player "station" would be ready for a player to join in and play.
Now, I don't know of ANY 2 player games which also did this other than perhaps some driving games like 2 player Super Sprint?
The reason most 2 player games even have 2 slots is not so that 1 slot is for 1 player, and the other is for player 2, but because it is better for "business" to have 2 slots in case one of them becomes defective, or for that matter sometimes a quarter that doesn't work in one side, works in the other. it just made more sense to the game's operator, because with one slot, if it broke, that's it, the game stopped earning money until the operator came by or someone called in to have it fixed.