One of my coworkers was fantasizing the other day about starting a company where they don't send any internal emails. His plan involved prioritizing face-to-face communication, dedicated Slack channels, and a suite of tools that made it easier to index, and search across Slack. It was an interesting thought experiment, but it broke down in a lot of areas, and I think our conclusions were:
1) It would only have a chance of working in a small organization with a single team, or few teams that communicate regularly and effectively.
2) It's one thing to favor other channels of communication, but outright banning of email didn't have a lot of benefits other than forcing people to favor said alternate channels.