Read on Twitter
The real reason there is so much objection to idea of permuting equal co-authors is not, as so many are saying, the sanctity of the bibliographic record must be preserved. It's because equal co-authorship is, in most cases, a complete lie. https://twitter.com/AdrianoAguzzi/status/1340704460667056128
As a computational biologist postdoc I was often 2nd or 3rd among "co-equals" on papers as part of a strategic calculus by my PIs that first authorship was worth more to the experimentalist who had all their eggs in one basket than it was to me, who was involved in many projects.
I understood the motivation, but I was nonetheless a bit annoyed that we didn't have a way to represent multi-author contributions fairly. So I proposed back in like 1999 to PubMed that they randomize the order in which ostensibly co-equal authors.
It's a trivial thing to implement. But pretty much everyone hated the idea - and as @AdrianoAguzzi is finding out, they still do. And I think the objections now, as them, are really about threatening the delicate balance often achieved with co-first/co-last authorship.
Because in the several dozen times I've been involved either as "co-equal" author, or in managing such cases, there has ALWAYS been a logic to the order amongst these co-authors.
Often it is, as it was when I was a postdoc, about who would benefit more from prime billing - being first first rather than co-first, or last last rather than co-last.
It still remains true that computation scientists often get the short end of this stick. But our internal evaluation systems have adapted - we know that co-first for a computational biologist means they did most of the analyses.
Similarly, when I was a new PI my senior co-authors on collaborative projects often gave me the last author slot on papers that were true joint efforts because it meant more to me than to them. And I have done the same as a senior PI.
And then there are the very common cases in which co-first authorship is used as kind of a consolation prize when the relative order of contributions is clear, but where "middle author" doesn't capture someone's contribution.
The point of all this being that if co-first actually meant truly equal and indistinguishable contribution nobody would care about randomization outside of a few lawyers/pedants like @mnitabach.
There is a real problem with accurately conveying author contributions in scientific works, but I don't think this kind of kludge solves it because it would undermine a bunch of other kludges that have evolved within what is ultimately a dumb system.
We need instead to come up with something better.
