That would be a solution if it were not for the 24/7 reliance on Slack for almost all team communication. I really really hate Slack-like in-your-face-all-day interruptions. It's hell.
As CTO, you get to set the communications culture of your team.
You should announce that you will check your slack notifications once every two hours and no more. Anything more urgent - come to my desk. Anything less urgent - schedule a meeting for tomorrow.
If people start abusing the “come over to my desk” loophole, start explaining to people what urgent means.