The fundamental conceptual problem with the Fredkin-like physics (<plato.stanford.edu/entries/computation-physicalsystems>) is that it puts the cart (of mathematics and computing) before the horse (of matter and energy). Physics precedes computing (and mathematics), not the other way around (as Tegmark’s “mathematical universe” has it). Another way to express the alternative (putting the horse before the cart) is by what I have called codicalism: Epistemology is computationalist; Ontology is physicalist.
re: … “a Fredkin-like physics based on some sort of universal automaton makes no sense unless a source of energy is provided for the cells.”
So I take the view of putting the horse (of actual physical substrate, aka “reality”: matter/energy/whatever) before the cart (of any mathematical or computational language, including HoTT, which is just another language, and there could be “better” ones 50 years from now).
Putting the cart (of math) before the horse (of physics) is platonism. Putting the horse before the cart is pragmatism.