would you agree that they don't have rules which specifically ban or suppress or mention recursion in order not to use it?
Yes, absolutely. I don't even need to go past English to find structures that we don't use for no apparent reason (ie. the structure will get marked as 'odd' but not flat-out wrong by native speakers, and the meaning will be completely intelligible), so it's plausible to me that a culture might just not like recursion in their language for no apparent reason.
[I'd put this in an open thread, but those don’t seem to happen these days, and while this is a quote it isn't a Rationality Quote.]
— Geoffrey K. Pullum, Language Log, “Never fails: semantic over-achievers”, December 1, 2011
This seems like it might lead to something interesting to say about the design of minds and the usefulness of generalization/abstraction, or perhaps just a good sound bite.