Echoes being so heavily objective-driven plays a big role in why they feel boring to play, because you spend more time running than fighting.

I don't know how others play, but I constantly catch myself "rushing" to the end of the map where I suspect the quest to be.

Instead of taking my sweet time slaying monsters, I spend most of the time just running. That is worst during the campaign, bit persists well into regular and even empowered monoliths simply because so much of the loot and rewards are backloaded (is this even a word? as opposed to frontloaded) via loot chests, prophecies and corruption.

In my opinion we should be able to leave echoes when you slay enough mobs to fill a bar with stability and that's it.

All current quest types could be turned into random events that you encounter in echoes. You'd find gates that spawn waves of enemies or get randomly ambushed or Spires could spawn randomly and drop fat loot or have some small indicator that shows their rough location and they're protected by lots of mobs.