Even if it had a reward, meh.

Sounds like a terrible idea/thing to be totally honest.

I don't like speed runs much either, I'd rather if the dungeons just had an extra hard version with different loots. Like, instead of making so people run past the few mobs they didn't on a non speed run, why not replace the mobs with things that spam sleep/gravity/bind/etc and run extra fast, while not losing agro if you get too far away. Then for bosses, have them summon more mobs, hard mobs, and more often. And do w/e else to make it harder on top of it.

And there ya' go, it'd be a hard mode that isn't some corny protect the flag carrier kinda thing. Because let's face it.. As a dungeon objective, that sounds terrible. A real hard mode would be like having every person be that 'party leader', because if anyone of them strayed or died, you'd probably all wipe anyway. :P