This is spot on. You should blame the tool for mismanaged expectations if the tool inherently sets the expectations.
I'm just trying to imagine ways you could use slack and not set an expectation of having someone online to chat to. Use a bot to resond with "we'll get back to you when we can"? There's no option that doesn't feel like an incredibly frustrating experience for the user.
Other support chat tools have solved this for quite some time with a queue and display of estimated waiting time. You may not get an initial response immediately, but once an agent becomes available they're assigned the chat and do communicate synchronously.
In comparison, Slack has no way to indicate that an agent is already working with someone else in another channel, nor any good way to assign a specific owner--customer questions are dumped into a channel with X support agents as members, one of whom will hopefully respond.
What confuses me is that's just not my experience. I've seen and helped run multiple company Slack channels, and none of them regularly had instant responses.
I'm just trying to imagine ways you could use slack and not set an expectation of having someone online to chat to. Use a bot to resond with "we'll get back to you when we can"? There's no option that doesn't feel like an incredibly frustrating experience for the user.