The Joe Rogan part makes no sense to me. Only a fraction of the listeners of the podcast would otherwise go out of their way to read primary science journal articles. Reading those is a skill and requires background knowledge to be able to read between the lines, shared context between experts etc. Scientific articles aren't written for a lay audience.
Try adding one of those papers to Mendeley. Or, for that matter, get it by request from the author. Legal and often fast. Add that. See what Mendeley does with the CiteRef.DOI and CiteRef.URI fields...
There should only be one canonical DOI for any given article though--that's the whole point! I think the URI is also supposed to be to the "version of record" rather than wherever you happened to find a copy.
Are we talking about Mendeley or the general Elsevier paywalls? Seems like you are complaining about several issues at once: Mendeley's restricted features, Elsevier's paywall (that can be relevant even for non Mendeley users) and JoeRoganization, by which I guess you mean that his guests don't always confirm mainstream expert consensus (The Science).
Mendeley changes certain fields on import to always download its abstract PDF as the reference paper with a link to its paywall. In essence, those things are PDF archivers and citation managers rolled into one. If I were to send you my latest research and you'd import it into Zotero, you'd get a managed citation and my paper. In Mendeley you'd get a managed citation and a downloaded abstract version with CrossRef to their paywall.
The reason this happens is Elsevier's business model. And this business model both really wrecked Mendeley and, I believe, contributes to medical misinformation being more dominant in the world.
But Joe Rogan listeners aren't using Mendeley. These issues are separate, but you're angry at both and are somehow mixing them. The paywall can be circumvented via sci-hub. And more and more papers are now on biorxiv and similar.
And I don't think medical misinfo has much to do with Elsevier or academia. It's human nature, and the quality and degree of evidence-basedness of official communications doesn't really help.
Also, the words "misinformation" and "fact check" make my skin crawl.
If your conclusion is that the plebs is so dumb because they listen to Joe Rogan instead of The Science(TM), I think you're just digging in deeper.
Also, during the pandemic, many blue check Twitter accounts said it's a pity that so many conspiracy theorists and fake news believers are reading papers and playing around with data. They should just receive The Science, spoon-fed, and accept it, and too much thinking and reading hurts them. In other words, think about what you wish for. When other people are given access to data, they may reach different conclusions than the approved respectable media expert consensus.
Also, sci-hub exists.