Hello, long time Halo fan. I appreciate you taking the time to look at and consider my feedback ticket.
I think it would improve the player bases interest in completing more challenges by making challenges able to be completed regardless of it it is an active challenge or not. You could still give incentives to finish the primary list given to you (maybe more daily challenges with specific rewards that are much harder to complete?) or another approach would be to give extra XP towards listed challenges but slightly (or even significantly) less XP for completing a challenge that is not a part of your listed challenges.
A similar system to look back on for similar references would be Reach’s medal system and challenge system. It had daily challenges, and weekly challenges, along with the option to complete challenges that aren’t primarily listed first and the ability to complete medals for Multiplayer, Campaign, and Firefight. Medals which would award extra XP and credits (Reach’s earnable currency system). Maybe even add a monthly challenge which awards an even more rare or unique customization option.