That may have been a problem in Feynman's day, but today academic papers takeup negligible storage. The only limiting factor is the number of peer reviewers, I have no idea if there is a shortage of those or not.
Acceptance is less about storage space, but about gatekeeping for "quality". Which in turn is about what papers are going to get read, because nobody has time to read all of the papers. People rely on high-reputation journals to narrow down the time they spend reading.
The number of peer reviewers may be one limitation, but I think the main one is the number of readers. The hard limit is how much time readers spend reading. Getting access to that is hard.
Anybody can publish. You don't even need a journal; just put it up on your blog. But as with all blogs, the hard part is getting anybody to care that you've done it.
That may have been a problem in Feynman's day, but today academic papers takeup negligible storage. The only limiting factor is the number of peer reviewers, I have no idea if there is a shortage of those or not.