Definitely all roles should make an effort to manage their enmity, but at the end of the day content (unless it's Ultimate perhaps?) is balanced around tanks being in their tank stance and using the necessary tools regularly to maintain aggro. If any tank wants to go DPS stance just to maximize their damage output but then find themselves competing for aggro then something has to give, either the other players use their emnity actions (if they are available or not on cd) or the tank needs to man up and adjust as necessary. Maintaining aggro is the bigger priority than using the DPS rotation, which should only matter if you are aiming for a speed run anyway, and many DPS checks can be passed without tank assistance so it's not like you are doing everyone a favour.

Emnity actions are often optional for most roles, (aside from the few ones that are built in to other actions), while tanks have permanent access to them so it kinda says a lot on SE's part on what is and isn't the responsibility of roles. Make more emnity actions built in to others and players might actually manage their aggro more, especially those you meet through the Duty Finder.

Essentially emnity needs to stop being treated as a dick sizing contest on who can dps the most and if someone messes they up, they get punished by letting them die, it does no one any favours and only promotes toxicity because someone doesn't play how YOU want.