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Makes sense. But i don't see how this is related to OO vs FP then. Putting all your actions into a list is easy. Replaying is easy. The main problem is caching the state which can become tricky no matter OO or FP.
You're right in that nothing about this is specific to OO or FP. However, under this model, you really don't want your actions in the actions list to change after the fact. That means those actions in the list really shouldn't be modeled as "objects" with object-like mutable internal state and all. In fact, you'd probably need them to be as lightweight as possible, which means no sticking methods on them. With those…
FP brings a lot of interesting concepts to the table that are useful. But I doubt that people that screw up OOP will screw up less with FP
In the end competent and disciplined (in my view the number one attribute of a good dev) people will produce good software with any paradigm. Clueless people will cause problems no matter what the tool is.