The MOV-only CPU [1, 2] is probably about as close to this as you can get. If you think about it, every structured programming affordance is sugar for writing a state machine. MOV-only pushes all control flow into a state machine, and does so without using any branches itself. It's all MOVs all the time.

[1] https://github.com/xoreaxeaxeax/movfuscator

[2] https://harrisonwl.github.io/assets/courses/malware/spring20...