I don't usually leave feedback (you guys overall do a really good job) but I do have some suggestions this time because I've been grinding a bit much:
Don't make the challenges specific to a location, I think the best part of the first challenges was that we could go wherever we wanted to complete them. I also say this because the ones that require you to go to Plains of Eidolon or Orb Vallis might not be possible to complete for everyone, I know a lot of people who can't run the latter and can't change their PCs atm + some people find it a bit tedious (especially when the challenge is "complete x incursions on x place").
Elite challenges can and should go hand in hand with "elite" missions or "elite" enemy types, this is very much sorties (which has been handled well), arbitrations, eximus or even just specific harder enemies and nightmare missions (for example). I'm not against time/wave goals for certain endless types of missions though! but then those shouldn't be long enough that no one wants to do them (aka the one hour survivals).
Better word the challenges. There's some duality or vagueness about certain challenges which make one wonder if we need to do one thing or the other. For Kuva survival I found myself and others confused on whether we had to not use the life support capsules (not even for harvesting kuva) or if we just didn't have to use them as life support capsules. For the current exterminate challenge some people have wondered if it's without enemy detection (aka not being seen) or just not raising the alarms (and it's the latter)
On the friend/clanmate missions topic I agree with those who say people could just add some rando to play with for those missions, since both get the benefit of that, and then unfriend once the deed is done but I also understand the appeal of doing missions on public or solo. So I can't really say much on the matter... especially when I have friends who play so their comeback would actually benefit me and I don't want to be biased.
Last point! I'm sure you guys have gotten feedback on the riven challenges so while I'm out of ideas for now, you could take a look to those. The riven challenges are not awfully terrible overall and maybe it would give some people twice the reason to do a challenge (say for a riven AND a nightwave act).
NOTE: this is specific to the challenges, I've just seen some people talk about the rewards and the gate holding and I gotta say being an experienced player I completely forgot about that and it can turn into a big problem.