Somewhat amusingly, I wrote a paper in 1991 that makes exactly your point. (The linked page at the journal is paywalled, but you can find it if you poke around a bit.)
It was about systems with more than one decomposition into modules, for which there had to be multiple simulations. Those simulations had to be compatible in a certain way, and that led to exactly the commutative diagram you have above (figure 13).
Somewhat amusingly, I wrote a paper in 1991 that makes exactly your point. (The linked page at the journal is paywalled, but you can find it if you poke around a bit.)
It was about systems with more than one decomposition into modules, for which there had to be multiple simulations. Those simulations had to be compatible in a certain way, and that led to exactly the commutative diagram you have above (figure 13).