To declare that "everything is choice" strikes me as putting one's beliefs ahead of inquiry.
Remember that mathematics is just a model, not the territory. For starters, you have incompleteness; for any formal system you can make true statements that are unprovable. Additionally, two constructs which are central to mathematical analysis, infinity and truth, don't exist.
For hundreds of years epicycles were used to model the orbits of the planets. Now we're elevating grand theories that embed the universe in an 11-dimensional manifold.
Due to Bell's theorem, we know that either there is inherent uncertainty in the universe, or the whole bedrock of science gets called into question. If properly informed by physics, the view that we are robots must follow from the view that the uncertainty in nature is uncontrolled, i.e. purely random according to some distribution. Given that we have a subjective experience of choice, this presents the alternate hypothesis that the uncertainty is the result of choice constrained by preference. These aren't the only two possible hypotheses, but remember that all hidden variable models have been effectively ruled out, so no deterministic hypothesis is permissible. I would of course love to hear any plausible alternatives you could present.