Yeah, this is the intuition I've come to, particularly after reading Quantum Computing Since Democritus. If you'll let me be slightly hand wavy, you can get to

Yeah, this is the intuition I've come to, particularly after reading Quantum Computing Since Democritus. If you'll let me be slightly hand wavy, you can get to Quantum Mechanics by generalizing probabilities in two steps: allow them to be negative, then allow them to be complex. Negative probabilities are quite unintuitive but seeing them as an accounting placeholder similar to how negative numbers are vs counting numbers helps it all click imo. The other big thing is that if you want algebraic closure you need complex numbers or something isomorphic to them.