I liked the idea of permanent weekly challenges back when they were something extra. Now that they're replacing normal weekly challenges, I worry they only make nightwave worse. There's just less variety now.
Having two different versions of "kill x eximus enemies" this week exemplifies that. Perhaps Eximus Executioner could replace Eximus eliminator when it shows up in rotation to make room for another weekly challenge. I also dislike "mission complete" because it discourages staying for a long time in endless missions.
If DE's concern is players completing Nightwave too quickly, I would suggest going back to having 10 weekly challenges, but having the permanent ones count for less standing (2,500 for example).