Go one level deeper and you'll find the problem with all of academia (source: I have a PhD).
Most of academic science as we know it today is structured so that the output is "publishable" and/or helps future grant applications. Incremental improvements are very publishable, but that doesn't necessarily make good science. Grants are awarded to scientists who are consistently able to deliver results, in the form of published papers. I can only really speak for my little corner of science, but from my view, the entire incentive structure of science is broken.
Incremental publication seems like a great idea. The only problem is that the publication process is so formal. But if we made publications as "blogs" or something, I think incremental units of forward progress are a reasonable way to do science. I suspect most science is done this way. I imagine there are few Wiles style FLT proofs around.
As the parent poster states, the key thing is that everything is structured about incentives conditional on delivering measurable results e.g. the quantity of published papers; but that implicitly includes a very important thing that "published" counts only if (and because) it has passed certain filters. There are no barriers to publish research outcomes as "blogs" or something, it is easy, so such "publication" doesn't imply that any reasonable research was done, and no incentives would reward such publishing, and that's why researchers often don't bother with it.
Like, the existing system already has issues with publication being too easy to game, with predatory paid journals, lax standards for reviewing, etc; that's hard to fix, but it's considered a problem - and so any changes making the barrier to publication even lower than that won't be welcome.
And from the perspective of researchers, we don't really want more publications - they're a pain to read, there's an overabundance of poor content that's salami-sliced, we do so many publications because the incentives push us toward this but we recognize that this is a bad thing and we'd be far better off if the same research would be published in fewer, better articles. But we can't, because anyone who does that will be effectively denied resources for future research.
it would also help us move away from the PDF to a web based medium, pdfs are generally suboptimal if not awful reading experiences for a scientific paper
Your argument is essentially that scientists, especially early career scientists, have very little room for failure. I would argue a central problem is that many grants for early career researchers have award rates below 10%. This is problematic because at some point why would you blow away a month of work to write a proposal that you gave a tiny chance of receiving. If the award rates were 20-30%, then you have more room for failure in the interim between grant awards.
Most of academic science as we know it today is structured so that the output is "publishable" and/or helps future grant applications. Incremental improvements are very publishable, but that doesn't necessarily make good science. Grants are awarded to scientists who are consistently able to deliver results, in the form of published papers. I can only really speak for my little corner of science, but from my view, the entire incentive structure of science is broken.