I imagine you're correct about course correction speed, although I'd also expect that the materials and their properties are quite classified at present.
I would also imagine that there could be processing necessary that is mostly unrelated to manoeuvering speed (inlet/control surface management, etc). Perhaps some hypersonic experts could weigh in and let us know :)
The theoretical limits of materials science is undergrad chemistry. Among other things, the bond energy between atoms in a molecule tells you how much energy is required to break them. The strongest possible bond is less than 3x the energy of the ubiquitous carbon-carbon bond of organic chemistry. There is a bit more to it than this e.g. the lattice structure also matters, but you get the gist. You can specify an energy that is not particularly high that is known to exceed that required to destroy all molecular materials.
Real materials are considerably worse than theoretical and you also have to optimize for other properties. The classified part is often more about the processes for fabricating specific materials. This can be extremely non-obvious and difficult.
All the exposed surfaces of a hypersonic missile are themselves limited by material physics. A major problem in hypersonic research was material surfaces degrading so quickly that they lose precision of control. The CPU can send commands but the physical materials of the guidance system don't respond in a reliable way due to the material degradation.
I would also imagine that there could be processing necessary that is mostly unrelated to manoeuvering speed (inlet/control surface management, etc). Perhaps some hypersonic experts could weigh in and let us know :)