Why multiple quantizations

Why can there be multiple quantizations of a dynamic system at all? (I.e. Mathematically)

why are there not physical reasons to prefer one over the others?

-- different choices of canonical variables yield diifferent quantizatations. Quanttiaa tigon and canonical transforms do not commute

😊 I think that it is the connection. Under different parameterizations the way that a local coordinate system moves is different. The zoevi-Civita connection buries most of this complexity and makes it connection look flat?

💣 but I would think that the inherent complexity is unchanged. You are just shuffling it around between parts of the parameterization...