I don't agree all the time with Ellatrix, but that's exactly what should be done in this case.
Yeah I vote for saving the chests for yourself post-run unless the party members vocalize wanting to get them- more for you that way. I've run WP on SMN in particular quite a few times so that as soon as the other three players are out the door, I pull out my 10k+ HP Titan-Egi tank pet instead of Garuda, and run backwards to the chests with relic parts that no one opened. Titan takes all the mobs in the areas we bypassed (at least some of which are bindable as well if I recall correctly), and if he kicks the bucket for some reason while I'm opening the chests I can just summon a new one. Easy solo chest runs on that class once the bosses are dead and the other party members gone.
I love when there are useful coffers (not potions) left behind. That just means that I can have the contents uncontested later (as long as I remember)!
This! My reaction when I run WP via DF and everyone skips chests because they are in such a hurry.
http://static.comicvine.com/uploads/...-good_good.jpg
I've also gotten a few mid level Brayflox rings by doing this.
I used to think that too...till I discovered WP :3