But not everyone does the crucible bounty and some players would like a weekly quest instead of a 15 mins mission. I do the bounty but could not care less about trials. Nightfall is the only non-PVP reward outside of a raid available.

There is. It's called "The True Meaning of War" (Complete all 5 of Lord Shaxx's weekly Crucible bounties) (for some reason, Trials and Iron Banner bounties actually count towards this.) it gives you Nightfall level rewards, including the weapons that can drop from random crucible matches. (Party Crasher+1, Red Spectre, Eyesluna, etc.) as well as exotics, ghost shells, or 18+ strange coins. Unfortunately, it's just like Nightfall rewards in that 90% of the time it's ghost shells and strange coins. Now that I think about it, Trials has a nightfall level reward bounty as well. The "gold tier" reward bounty.