If you are going to include formal proofs with your AI showing that the code does what it’s supposed to, in the style of Coq and friends, then the characteristics of traditionally unsafe languages are not a deal-breaker. You can totally write provably correct and safe code in C, and you don’t need to restrict yourself to a sharply limited version of the language either. You just need to prove that you are doing something sensible each time you perform a potentially unsafe action, such as accessing memory through a pointer.
This slows things down and adds to your burdens of proof, but not really by that much. It’s a few more invariants you need to carry around with you throughout your proofs. Where in a safer language you may have to prove that your Foo list is still sorted after a certain operation, in C you will additionally have to prove that your pointer topology is still what you want after a certain operation. No big deal. In particular, a mature toolkit for proving properties about C programs will presumably have tools for automating away the 99% of trivial proof obligations involving pointer topology, leaving something for you to prove only when you are doing something clever.
For any such property that you can screw up, a language that will not allow you to screw it up in the first place will make your life easier and your proofs simpler, which is why OCaml is more popular as a vehicle for proven correct code than C. But if you are proving the correctness of every aspect of your program anyway, this is a pretty minor gain; the amount of stuff there is to prove about your object-level algorithms will be vastly greater than the requirements added by the lack of safety of your programming language. If only because there will be specialized tools for rapidly dealing with the latter, but not the former.
Not all those specialized tools exist just yet. Currently, the program correctness proof systems are pretty good at proving properties about functions [in the mathematical sense] operating on data structured in a way that mathematicians like to work with, and a bit rubbish at everything else people use software to do; it is no coincidence that Coq, Agda, Idris, Isabelle, and friends all work primarily with purely functional languages using some form of constructed types as a data model. But techniques for dealing with computing applications in a broader sense will have to be on the proof-technology roadmap sooner or later, if correctness proofs are ever going to fulfill their promise outside selected examples. And when they do, there will not be a big difference between programming in C and programming in OCaml as far as proving correctness is concerned.
tl;dr: I don’t think language safety is going to be more than a rounding error if you want to prove the correctness of a large piece of software down to the last bit, once all the techniques for doing that sort of thing at all are in place. The amount of program-specific logic in need of manual analysis is vastly greater than the amount of boilerplate a safe language can avoid.
This is really helpful—thanks!