The simplest processors use one clock per instruction with a Harvard architecture. This allows their control unit to be a combinational circuit instead of a Finite State Machine (and depending on how your memories work you might even avoid having an instruction register).
Most one-instruction processors take multiple clocks and often need extra registers (for fetching 16 bit addresses from an 8 bit wide memory, for example) [1].
The four instruction MCPU [2] is not as bad to program as the one-instruction computers (it still needs 10 times as many instructions as a RISC-V, for example) while being very simple. Making it Harvard allows it to be slightly simpler and making it 16 bits allows it to run non trivial programs [3].
[1] https://github.com/jeceljr/SBN/blob/master/sbn.pdf