The stack is one of those things that would fall under "support for common paradigms". I checked that PDP-11 (the machine on which C was created) already had a hardware stack - and probably even older machines. There are many other programming languages that have the concept of a call stack. Hardware stacks are just an optimization to support this paradigm, and you are not required to use it. Conversely, C does not require any hardware support for implementation of the call stack.

The main problem with hardware call stacks is that they can't be relocated if you need predictable performance and/or have pointers instead of offsets into the stack. That means they are bounded size. With 64-bit addresses that may be less of a problem, but still. Functional language do not need to use the hardware stack, so that shouldn't be an issue.

> Having a single address space for both code and data mainly just gives an opportunity for optimisation to fail.

I don't think C requires that in any way, but since void pointers are allowed to point to either code or data, representation of void pointers must be somewhat "compatible" with both address spaces.

> Everything-is-mutable gives a lot of opportunity for optimisation to fail.

Not a hardware issue. Also not everything is mutable, not even in C. But you need some mutability for performance even at more abstract levels.