Remote / Async work without chat?

My team uses Slack quite a bit, but I don't feel it's actually working well for us. Too many decisions and task requests are made in chat, and then there isn't really a permanent record of them. We're not a very big team, but we already have too much reliance on humans plus meetings to share context and make sure everyone is on the same page.

My gut says we'd be better off without chat, but I think that if I just turned off our Slack instance we'd end up falling back to SMS and Email for quick pings, rather than really improving the situation. I would like to build a culture of thoughtful async discussion where people organize their ideas in writing, but I've never been part of an org where that was prominent, so I'm not very confident how to establish that from scratch on my own team.

I'd love to know if any of you have experience working in a distributed engineering org that doesn't use chat, and if so, what tools and processes do you use for discussions and keeping shared context? How well does it work, and would you recommend it for another team?