So I've done that. I've asked dps not to pull extra packs because I'm already handling what I can handle (or what the healer can handle through direct observation)... more often than not I get told off for speaking up by the very same dps that was pulling extras in the first place.
Bear in mind you're making some assumptions here that, while they sound reasonable to you and me, aren't valid. The primary assumption being: the entire party is willing to listen. This is just categorically not the case. If someone has already decided to take it upon themselves to put extra pressure on the party, they've already made the decision that their time is more valuable than everybody else's and confirmation bias will prevent them from hearing anything that tells them they're wrong.