If +burst is being prized on weapon skills, then it's because DMM players seem to be hunting for whatever that can directly increase their burst damage. It's really just assault, pride, exceed, and stinger that do that. Stinger assumes that you're going to be leveraging elemental advantage, so I'm assuming here the DMM players in question aren't rocking endgame teams of all elements. The +double and +triple skills would increase the rate at which you can burst over the long term, but not the damage of any individual burst. Said players presumably aren't all that worried about frequency of bursts. Nor do they seem to need +HP or +healing.

What I'm curious about is, whenever vigoras (think opposite of pride) gets implemented, would players want that? If vigoras as a weapon skill actually applies a ousei/vigorous buff, then things get interesting. Ousei/Vigorous is listed as something that gets counted in otherBuffs. (if you don't know what direction I'm hinting at here, go back to the normal attack damage formula).