Decision-making in writing in the 21st century! Are you serious?

You bet. It may appear to be slow and cumbersome at first, but once you see the results in terms of reduced meetings, reduced challenges of synchronous communications, greater clarity of thought and the power of a record based retrospective, there will be no going back. To know more, please refer the chapters on accountability and communications in the book Agile IT Org Design.
What is the state of the art? Meetings. Yes, we decide things in meetings (or through meetings). We know how well that works out:

It gets all the more entertaining with video conferencing technology:

Hope that's enough motivation to try something different (doing it in writing). Verbal, meeting-based, decision making may sound as natural as creating a slide deck to make a pitch. And then we see the way Amazon does it. Jeff Bezos explains why:
Well structured, narrative text is what we’re after rather than just text. If someone builds a list of bullet points in word, that would be just as bad as powerpoint.
The reason writing a 4 page memo is harder than “writing” a 20 page powerpoint is because the narrative structure of a good memo forces better thought and better understanding of what’s more important than what, and how things are related.
Powerpoint-style presentations somehow give permission to gloss over ideas, flatten out any sense of relative importance, and ignore the innerconnectedness of ideas.

A similar kind of executive backing is need to move to a culture of deliberating in writing for serious decisions. It may not be easy but it is certainly possible.