That’s not the conclusion, that’s the whole thesis. The whole point of it is that yes, it’s not provable, but so far we haven’t seen anything to suggest the contrary. All of our current physical theories are very much computable, for example.
And we know that we can define an infinite amount of problems that can not ever be computed (or else you can for example solve the halting problem). So there would be infinite amount of questions about the world that we can not ever answer.
And there would be more questions that we can not answer (they are uncountable) than we can answer (they are countable). So if you have a question - chances are such that it can never be answered.
edit: more likely never can be answered.
Like I said all current theories are based on current state of observations. Who is to say we don't observe something in the future for which these laws need to be revised? Who is to say this doesn't keep happening indefinitely? If such a "bottoming out" cannot even be conceived of, saying that the physical world, even a part of it, is exactly computable AS IT IS (all aspects of it) is utmost arrogance.
What do we know about the brain? how does it generate cognition? why does the color 'red' look like the way it does to you; does it look like the same to me? Unless the nature of such cognition and such a being which embodies this cognition is known one cannot say it is reducible or "emergent" from the CURRENT set or even any FUTURE set of physical laws we know or will know about.
The map is not the territory however minute in detail it becomes. Sure this map can become the territory itself by becoming it but then we cease to call it a "map". Say you want to understand how pendulums work, you make a pendulum, play with it. No one's going to call this actual pendulum a "simulation".
Also our physical theories are only computable with an arbitrary halt thrown in at some level of accuracy deemed good enough. And there too theoretically questionable trickery like renormalization is used to reduce the problem to a tractable size.
How did you get to the conclusion that all physical world is computable? Rather a huge jump i would say. Sure some things are, but "all of it" would rather be a BIG assumption. Physical theories of the world are limited to our current state of observations and knowledge of the world, they AREN'T the actual world. Who is to say this continuous search, observation and refinement of theories will ever end and we'll have a FINAL theory of everything that we can then plug into a computer and simulate?
Sure you can now say "I don't require a theory of everything, I just need a "sufficient" amount of theory to simulate the part of the world from which I can have my intelligence & cognition emerge". Sure you can say that but that would again hinge on the assumption that such cognition is reducable to these "sufficient" laws.
Likewise saying that the whole physical world can be realized by a Turung machine is a bit rich when we don't even know if such a complete reduction of the physical world is possible and when such reduction to physical laws is surely not yet complete.
EDIT: grammar