FP is a tool. It has potential to solve some problems. That potential won't be wasted, but the problems it will solve aren't the problems you have in your world.
On the other hand, FP could be just fine for writing the tools that will help you in your world.
You want uniqueness typing that allows you to have functions that modify the variables without breaking the functional abstraction in straight forward manner. You could also reason about the memory use and have fixed amount of memory. Ordered typing would be nice feature to have. You also want hooks in the compiler for a additional tools for static analysis and proof assistants.
Recursion itself is not bad idea. It's strictly forbidden in safety critical code today for reasons that can go away. If you allow recursion, compiler must be able to reason and define the limits. Recursion is not good idea in safety critical code when it obfuscates the execution, but that is not always the case.
Raw recursion or recursion using recursive schemes?
My turn: What's a recursive scheme?
That's why we need more Haskell-hosted system programming DSLs - with fancy sound types, proofs, extraction and stuff.
As someone who has written safety critical software where you are willing to pay big buck for verification tools and software, Haskell has done nothing. I would love to use Haskell type FP but people who work with Haskell are thinking about correctness abstractly and real world (and earning lots of money) is not their priority.
All talk about correctness, absence of runtime errors are futile when you limit your definition to errors you want to deal with and ingonre the rest.
Having sound type system means nothing if you can have runtime memory errors, can run out of stack, pause for GC too long, don't know how much memory you may use in the worst case, can't detect divisions by 0, or float/fixexd point range errors ... etc.
Writing MISRA C and using verification tools like Astree, or SPARK + verification tools are not as elegant, but their weakest point is stronger than Haskell's.
If I sound salty, it's not because I think FP is bad idea, it's because I think the potential is wasted.