It makes zero sense within the universe.
IIRC their excuse was basically TNG canonically said that Klingons had a whole bunch of redundant organs (including a second spine) so they decided "why not two dicks as well...lol!"
It's interesting they appeared (based upon the urine streams at the end of Season 1) to put them up-and-down, rather than side-to-side as is the case in living animals on earth that have two dicks, like snakes. It must mean that someone in the Discovery writer's room has some odd fetishes.