I am also wary of people suggesting that software whose users are "required" to pay a per-user fee could be open source. Open source software could not come with a universally enforceable requirement of this kind. "The license may not restrict any party from selling or giving away the software..."
But the prospect of open source developers being paid other than per-copy, per-user is plausible. Alex Tabarrok demonstrated in 1996 that it should be possible to do it even without altruism given enforcement of contracts and someone with sufficient information about demand. (I don't know if that kind of information is often achieved in practice.)
Karl Fogel just ran a successful Kickstarter campaign to fund creation of the second edition of Producing Open Source Software, which will be distributed on terms closely parallel to open source software (all recipients of the book can redistribute and modify it, and nobody is required to pay a per-copy license fee). The payment to Karl happened up front and ahead of time. The same structure might have worked if Karl were to apply this funding to software development instead of to writing about software development -- and indeed Joey Hess did that a while ago with his git-annex-assistant Kickstarter, which as far as I know has worked out quite well.
In the Kickstarter case there is a significant potential free-rider problem; for example, I didn't personally fund Joey's project but I might still benefit from his work on git-annex. Kickstarter seems to use various aspects of social norms and psychology to address free riding, often with good results.
I think we need more work on this even as we continue to insist on not diluting the meaning of open source.