Using specialised meanings for words without definition or reference (words that are used for other purposes elsewhere so they can't be searched for) is a key problem, as is the same with notation, and as is leaving out crucial steps. If you're already in the know, those things are probably clear.
The perfect case would be if someone is great at research and also great at explaining. But great skills are rare, and specific combinations of great skills are even more rare. So you will have a scientist or two who are great explainers at the same time, but then you have a lot of scientists who are great at research but suck at explaining, and also a lot of people who are great at explaining but suck at research. How does academia reward them?
The ones with both skills will get the highest rewards: they will invent lots of cool stuff and describe it clearly, so they will get many citations. But there are only a few such people per generation. The ones who are good researchers but suck at explanation can still invent something and publish the type of paper you complain about; and they will get a (smaller) reward for doing so. The ones who are good at explaining but suck at research... will probably be fired.
There are a few things that a person whose only skill is explaining could do in academia. They wouldn't get a reward for explaining someone else's paper clearly, but they could get a reward for writing a meta-review that would explain multiple papers clearly. In theory, their scientific contribution would be in comparing the papers, but in practice, hopefully even people who only needed one of the papers would cite them as a reward for making it easier to understand. -- I don't know if this would actually be sufficient to survive academically.
People who are good at explaining can also make money by writing popular textbooks. Question is, whether there is a sufficient demand for a popular textbook explaining some obscure math.
I see tremendous value for such work, and I think it is one of the biggest current bottlenecks in the sciences. We've got the cutting edge stuff happening in papers, and we've got 5-10 year old knowledge that makes it into textbooks, but in the middle there is nothing. Everyone is working on their own to catch up. We're talking thousands of grad students independently banding their heard agains the same problems...
If there were more "review journals" things would drastically improve. Maybe NSF could provide some funding for such efforts? Not sure what the metrics would be for this---not citations, we'd nee more like views or upvotes like on HN. The other option would be for grad students to self-organize into "reading clubs" on different subjects and share notes.
I'm not sure if explainers-first are the minority, though. After all, it's much easier to review than to create. And we do want new research.
But, I would move away from papers entirely. They hold no redeeming values over alternatives like a git repository published publicly with an "issues" forum e.g., GitHub, etc. This needs to absolutely become the new standard, and we need to get rid of papers and journals, both physically and digitally, in their entirety. They have zero redeeming factors at this point in time except to boost the ego of the published. Quality control can easily be decentralized and available to everyone using something like GitHub. We know this because that is literally what the security and trust of open-source software is predicated on: putting everything in the open.
If I tell you B = (dA_z/dy - dA_y/dz)i + (dA_x/dz - dA_z/dx)j + (dA_y/dx - dA_x/dy)k do you instantly see what operator is applied? That's why you just write B = ∇×A.
People presenting ideas in shorter notation is not showing a lack of progress - usually it's the opposite. In old optimization papers people would write out the entire normal equations, entry by entry. Not really insightful at all, compared to A'Ax = A'b.
To that, I'll add anecdote. Some years back, I had a fight with a coauthor on a paper who wanted to remove the majority of the substeps within a proof. He believed that it was condescending to include such material and that any interested reader should be able to derive it for themselves. And, in fact, he asked a colleague in the room at the time who agreed with him. I stated flatly that as the primary author that I could not understand nor complete these proofs without these steps, so the material stays. I contend that at least in this one particular case a combination of exclusivity and arrogance led to an attempt at obfuscation.
Remember, publishing isn't just about sharing knowledge. It's also a way to posture, advertise, build a brand, and get grant money. Beyond that, mathematicians are still people with all the imperfections that implies.
At the same time, it doesn't mean there's a concerted effort to obfuscate mathematics.
Explaining things is hard, because you have to create a clear picture of the audience in your mind. Then, you have to draw the lines between what they know and what you want to introduce. The curse of knowledge is a big obstacle here.
The other thing is at the time yes, people who could read and write was a small minority. That have been the case in other societies with writing too. Not because of a cabal making it difficult but because getting an education was very costly.