The part with the mistresses--yep, that would be hypocrisy, which comes from an attitude from those in power that they think they're above the system.
The other part...I do think the Cardassians see it as "consistent" by their values, but obviously it is not from an outside standpoint. I would also add that I do not believe we've seen any proof that other relatives aren't required to take in children when the parents died. The trouble may instead come in when relatives are ruled unfit, or do not exist. In those cases I suspect the state does not want to spend resources on those children, and while I agree with your point for what is TRULY right (that those children could easily go on to do something right), my point is that within the Cardassian system
it is consistent with the state-ueber-alles mentality, up to and including the idea that some people should die or get by on a bare minimum for the good of the rest.
Again...do I agree with that sort of decision? Do I want to see that for real? HELL no. Do I think it is consistent from an OBJECTIVE moral standpoint? No. (And do I think all Cardassians buy into the idea? No.) But from the Cardassian state's
standpoint, it is.