What are CPU designs which are not fetch/store but operate directly on RAM?
I only know about the design of the Nintendo Entertainment System (NES), where the CPU does not have registers (AFAIK) and operates directly on RAM, with fast access to low addresses in the RAM.
What CPUs/Systems do you know, which also do not do fetch/store for their operands? Which systems are out there? Why do CPUs like RISC/Arm/AMD64 use fetch/store, what are the tradeoffs? Are there different architectures for CPUs working on operands outside of fetch/store, DMA and stack machines?
Interesting question, a lot of CPUs have instructions that act directly on memory, but not having any registers would be a weird kind of system. You could design one for yourself en run it on an FPGA, but it probably wouldn’t work very well. At the very least you would want to have an instruction pointer and accumulation registers.