I think big persistent groups sometimes do help with that. If you want to know which client requested X, then messaging one person is slow, and walking up to ask one person is disruptive. With Slack, you can ask 30 people and get an answer from whoever looks first (and so presumably isn't disrupted). Everyone else who's busy ignores things and skims things when they're not occupied.
That's all contingent on a culture of async Slack usage, but I've found it valuable.
I don't get it. Doesn't any popular chat client fit the bill? The thing Slack adds is big persistent chat groups which doesn't help with the problem you're describing.