So, something I've honestly wanted to see even in JP is having quests that are designed like Challenge Mode in the main game to play with our actual gear. Time attack quests followed this idea a little, but were pretty niche. Even though they had the Falspawn den chance and COs for more money at one point, they really weren't that meaningful as far as unique things to get from them and were very obviously never the main content. And even so, Time Attack quests were never really made to the scale of Challenge Mode quests.
I think back to things like Phantasy Star Universe. This game wasn't perfect with its missions either, but I think overall its kill to progress mission structure combined with some of the puzzles its missions had were cool and a bit more interesting compared to the somewhat mindless run in a circle or "guruguru" quests , as the JPs called it, that PSO2 is known for.
PSU had a lot of interesting ideas with its gimmicks in quests, particularly in events later on. One I always think back to is Protectors Epsilon here: https://youtu.be/EiOB_QMl3G8
The mission structure is linear, but the players are restricted in what weapons they can use and unlock more weapons back as they progress.
In addition, there was a bit of a community puzzle the players needed to solve to get the most and rarest drops in a run, a bit of a theme in PSU event missions. Players often had to collaborate to figure out what the various clues to the particular patterns in their quest meant so that they could unlock the extra drop chances. It's not really something PSO2 did with quests, at least before I stopped playing JP regularly around episode 6.
I think they tried to move in this direction a bit with things like the Armada quests, but it's not quite the same. Still, I'm excited seeing the experimentation. I'm hoping Not Episode 7 has some of these ideas in it or perhaps something new and different to all of this.
Edit: Random suggestion for another quest type, but a pvp mode where players go against players who control enemies would be pretty cool. I'm imagining something along the lines of Star Wars Battlefront 2 where the players controlling enemies build points and can bring in higher leveled/stronger enemies as they progress through the match, but can also bring in higher tier or perhaps "hero" sort of units such as maybe a boss to play as. All the while the ARKs players would be defending a series of objectives or pushing through the enemies for a series of their own objectives. The game has a lot of interesting enemy types that could be pretty interesting to play and with the right objectives, I think it would work well.