A couple of man-weeks to design and implement a CPU in an FPGA but from what I see, man-years to retarget the compiler.
myC has been 8 years in the making, there is no optimization layer yet and the machine layer only includes MIPS32 and MIPS5++ (prototype).
I personally spent some time on myC too to do some personal development and research and see what could be done to improve C.
Not much, I tried and... honestly, I tried so many ideas in the last 8 years, almost all of them miserably failed, except the latest approach that is giving me satisfaction, but not so much if we consider the generated code.
I think it's basically a matter of trade-offs, but finding the right balance in a C compiler, written from scratch and mutated, or simply cloned and retargeted, always requires experience and a lot of time and dedication.
Does it make sense? It depends, but if the goal is to run Doom, then I think it's better to take a risc-v core, a { binutils, gcc, gdb, musl } toolchain, and digest them as is.