I'm not gonna go into "easy to implement" because, honestly, I doubt it would be. I'm not a programmer, I just find it extremely unlikely that one line of code would solve it.

But other people have brought up a lot of good, valid concerns.

Mainly, I agree with what counts as "Next" one, though I do see that the original post says "Another" which could be anything.

That said, I'm also in agreement with how you can simply ask someone if they want to help you in more roulettes/MSQ at the end of the dungeon. If people are leaving too fast for you to ask, clearly they have no interest in staying.
Secondly, people who are looking for a consistent group of the same people can do it via Party Finder.

And as it has been pointed out, we have the contacts section where you can find someone you just went into a dungeon with. I don't really see how that is not enough to reach out to the people you've just ran content with, I've added friends and messaged people (And in one specific case, invited them to an Eternal Bonding Ceremony lol) through the contacts. But perhaps someone who finds it lacking could explain further what exactly are its shortcomings that I'm missing?

Overall, I find this a very redundant system at best. Disruptive at worst for example when you're going through MSQ, in the middle of cutscenes, or just need to go. Though I would love to hear suggestions of implementation to improve on those concerns that, honestly, go beyond "It can be done because WoW does it"