I feel it's up to the healer to decide when/if it is appropriate to do damage. Just like in the other roles, no one enjoys it when someone else comes along and tries to backseat drive them.

Granted, a healer throwing out damaging spells does help. Killing a mob prevents it from dealing damage to a party member. In addition, it's fun. Sitting around twiddling your thumbs all run is boring!

However, that healer "doing nothing" could be regenerating their mana or they could be taking a moment to decide if and what kind of healing will be needed soon. Triage is a big part of the healer's job.

That's something a damage dealer needs to respect. Because a healer is playing a different game than them.

A damage dealer is running a race. They are going all out to reach the goal tape.

Meanwhile, a healer is playing darts. They are deciding which target to hit and how much without running out of mana or overhealing.