(Not claiming that OP's work isn't absolutely cool, rather suggesting paths for future improvements. :D)
It's easy to construct parametrized boundary representations (as OP used) that maintain topological invariants, but it's very difficult to use them to explore the space of possible topologies (which would be relevant if OP wanted to say, design a lighter wheel).
This can be considered a generalized example of the bias-variance tradeoff. Imposing symmetry or a parametric form can be considered forms of regularization/bias that help converge to a well-formed solutions.
Yes, but you're always going to have a prior.
You could model it as, let's say, a shape in a square grid with a certain area. Or a collection of line segments that are closed.
This is an issue common to most optimization problems, you want the simplest model that will be efficient, otherwise you might risk overfitting (or just taking too long to optimize)
Could this way of representing the problem (radius) introduce bias to the solution? It could probably make many kind of shapes, but it may need to overcome some huge local maxima in order to drastically change it to something else by tweaking multiple of the radii.
When writing my thesis on spoke patterns for bicycle wheels, one of the representations outperformed the others, as it had symmetry baked in. That could have made it not find some esoteric solutions (which is why I had multiple representations).