Slack doesn't have to be synchronous.
I am part of hundreds of channels across 10 accounts. I only respond to notifications but will typically spend an hour or so at the end of the day just catching up on everything. With email I would simply never know these discussions were even happening.
You can use Slack this asynchronously, but if you do it every day, it might as well be static.
On the other hand, I only use one account at a time, for the most part: my work account.
For one, you can never guarantee nor should you expect your team to be colocated. Even if you have one office, people should be free to work from home. Side chats get lost, people forget or don't hear. Slack is public and searchable. No mumbling and if you mistype, you can fix it. Plus you can add documents, links, images while you're talking.
People say getting communication on their phones is like an anchor to their desk but I feel the exact opposite. It means I can leave my desk anytime I want and not be out of communication. If something critical needs my attention, I can answer while I'm home and not go back to work.
Sorry to say this, but if you are answering things on slack at home, you are "working" and anchored to your phone.
And then we started making our own clique chat rooms. Then it became mandatory to not have tech discussions in a clique room.
Am I old fashioned in thinking that voice to ear (or nearest equivalent) should have the role of primary communication channel?
I’ve been struggling with this lately, to the point where I’ve experimented with going back to a dumb phone, and trying to use my smart phone without Slack. As a remote employee, I think having Slack on mobile has lead to a greater degree of freedom, as you mentioned, but I also wonder if the constant tether is leading me to burnout more quickly.
Urgent things should be passed by audio (traditional VoIP phone call, not bound to any desk since we have mobile internet and softphones) non-urgent thing goes better via mail instead of wasting people time to look a chats.