My brain goes weird again

One of the sillier tropes of science fiction is the race of beings who "age backwards", who somehow come into existence as elderly and feeble and then become younger and younger.  If they are not literally going backwards in time relative to some other standard — moving backwards, perceiving in reverse, etc. — there are some obvious paradoxes.  The Red Dwarf episode "Backwards" at least had a degree of internal consistency, but the Animated Trek episode "The Counter-Clock Incident" was just silly.  (Alan Dean Foster's novelization of that episode lampshaded some of the problems.)

I had a strange thought: an interstellar empire of such beings.  Their starships' engines are driven by antenatal infants' being yanked back to their mothers to disappear.  Utilizing the power of paradox.