I'm not a hardware engineer, but my understanding is that some FPGAs include an entire cpu core as part of the chip? This seems much more efficient than designing your own.
Super small CPU cores are fantastic for complex FSM replacement, especially on an FPGA which has unused block RAMs (so using them is essentially free.)
I’ve seen cases with relatively complex pure HW FSM being replace by a small CPU and 1KB of RAM where the logic used by the CPU ends up smaller than the FSM.
But now the CPU is programmable, so you can iterate much quicker in case of bugs, without the need to reaunthesize.
A good example are SDRAM controllers: almost all of them have a small CPU inside the controller that is used for calibration training.
It's almost always more efficient to use an existing CPU if it fits your use case than to design your own. Even if it doesn't, it is often more efficient (time wise) to adapt your use case to the hardware you have available, or write software to resolve the feature you want in hardware but don't have. Only the especially nutty build their own CPUs (I'm especially nutty too)
The cheapest FPGAs are under $10 and many can fit a small softcore - usually not a full pipelined, cached + MMU RISCV core at 100+ mhz but enough to drastically simplify high level logic in FPGA projects. The Zynq series with onboard CPUs start at $40-50 in low volumes and have 1-4 cores at 600 mhz which is complete overkill for many FPGA projects.
