We rarely pick up a phone, and we do not use email. Everything is 100% Slack.
This works well for us. You can bring in only the people you need, you can "star" messages and channels that are important, and none of us have any time to spam/meme the channels, so it's 100% business. We integrate the JIRA slackbot to keep abreast of what is going on in JIRA.
It all "just works" for us.
My employer uses Slack. Our team channels are almost completely devoid of cruft. There are office/location based channels that contain more bloat, but those are easy to ignore and typically don't contain critical information. All of the "all employee" type channels are locked down.
If it is the primary method, you'll miss stuff.
Whether it should, is another matter, and running a one-man rebellion from within is probably not the most effective way to change that.