With an IRC- or Slack-like communication model, waking up to 100+ new messages every morning is a big drain on time and energy. Also, once a channel starts getting 100+ messages a day, it stops being useful for real communication. If someone starts a conversation at 10am, and you come by after lunch, it's hard to respond in context.
You can see how Zulip solves this problem on the Zulip community server, https://chat.zulip.org (send test messages to "#test here", follow the code of conduct, etc., it's a live server). Feel free to PM me there if you set things up and have any questions/feedback.
To address a previous post: Zulip, Mattermost, and Rocket.chat all take about 5 minutes to install, so I wouldn't worry too much about that. Zulip and Rocket.chat also come with SaaS versions if you don't want to run your own infrastructure.