Once a project takes contributions without a CLA, there can be hundreds or thousands of authors, many of whom are unreachable.
More money in the hands of F/OSS maintainers and teams will be the rising tide that gives us all even better ecosystems than we have now, I hope.
You can do it without copyright assignment by, for example, contributors granting the maintainer a license to relicense their contributions.
Also to more directly answer your question, the idea is that they sell a custom license to their own AGPL code -- if that code is mixed with code they don't own that is indeed a quandry! The royalty industry has a pretty well established model, so maybe we can use that.
Again I want to point out that this is probably not reasonable for library authors (for many other reasons as well), I'm mostly thinking of people who are making software someone might want to rehost.
Funny, there actually might be a business in here for managing the licensing and royalties for upstream projects in this future I'm envisioning ever comes true.