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laofmoonster comments on [LINK] If correlation doesn’t imply causation, then what does? - Less Wrong
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Looks promising, but requiring the graph to be acyclic makes it difficult to model processes where feedback is involved. A workaround would be treat each time stamp of a process as a different event. Have A(0)->B(1), where event A at time 0 affects event B at time 1, B(0)->A(1), A(0)->A(1), B(0)->B(1), A(t)->B(t+1), etc. But this gets unwieldy very quickly.
Your workaround is correct, and not as unwieldy as it may appear at first glance. A lot of people have been using causal diagrams with this structure very successfully in situations where the data generating mechanism has loops. As a starting point, see the literature on inverse probability weighting and marginal structural models.
Processes with feedback loops are, in fact, a primary motivation for using causal directed acyclic graphs. If there are no feedback loops, reasoning about causality is relatively simple even without graphs; whereas if there are loops, even very smart people will get it wrong unless they are able to analyze the situation in terms of the graphical concept of 'collider stratification bias'.