Hard disagree. The tank's job is to hold aggro and protect the team, not run off and leave stragglers behind because he needs to be the star who has to prove how ub3rl33t he is.
When you're playing normal content on a PUG you get all different kinds of ATs, builds, and levels on your team. Do not assume the rest of your team isn't going to get curbstomped by stray bosses you were too lazy or disinterested to go back and deal with. Also, why would you want to run into the next room/spawn if half the team isn't ready because they're dealing with the stragglers you left behind? That's not how a coordinated team works. That's how a tank who thinks they're special and doesn't need the rest of the team works.
I've been on a number of teams I've had to leave because the tanks refused to mop up before running ahead and the squishes kept dying because of it. It's not cool. And it's not fun.