The parameter count has not gone up; it's equal to or less than usual Bézier control handles, because I forced the parameters to take specific values.
The part that is "new" about the Béziers is the new formula that selects one specific Bézier out of all the possible choices. I think this linguistic accusation is silly; for example, if someone discovers a new rock, it would be fair to call it a "new rock" even though rocks have been discovered thousands of years ago.
These curves are also unrelated to the file format; the curves are designed to fit how the user thinks about curves rather than be computer-efficient. For the tooling point, I think you are agreeing with me while arguing; I agree that there's no reason the curve should match what is used in the final product, and some of the other curve choices I considered require a complex conversion step.