Telling players in advance would be better, but it would also feel ridiculous having to schedule around that. That starts to make it feel like a job again. They should make these exotic quests their own "event." Make the quest chain a little longer and have them active for an entire week. Black Spindle was really exciting when it was first discovered, but that is such a good challenge, they should make that available for anyone who wants to try it.
People who want to get on all Destiny: TTK content when it comes available already have to schedule around Destiny. You have to login every day to see if another time gate has been lifted for that day, and then use X hours to complete content if something time gated was unlocked. For that audience, which is most of DGAF imo, it's already scheduling thing and can feel equivalent to job.
Like yesterday when me and my friend were about to log out for the day we learned about NTTE quest being available. We knew we better do it all now and asap because we couldn't trust Bungie to keep it available after next daily reset, but felt that Bungie will put that back behind time gate switch.
Bungie hasn't made Destiny any more player friendly in this regard, worse in a way imo.
I also feel that questlines for exotic gear
[I expect those 3 exotic armors to be behind time gated quests] should be longer and meatier, and once activated either be available 1-2 weeks or just forever and become into Director after completing e.g. Taken Wars.