I actually agree with you about math education and math texts. It is really bad at conveying understanding and my math-heavy courses were the toughest for me (E&M in grad school was awful). Too often math textbooks simply present things and leave the proof as an exercise for the reader, or they will lean too far the other way and present formal proofs for everything. Either way is not helpful for developing an intuitive understanding of what is going on.
The things that helped me develop communication skills the most were simply doing it a lot followed by having some good mentors that I found to be good communicators. My grad school advisor was great at communicating physics and one of my early bosses in industry was an excellent presenter. So, I would often bounce either writing or slides off of them for feedback.
I am guilty of writing walls of text as comments, but I try to stick to my lane. You can see my most recent wall of text about freeze dryers as an example. There are a few things that I think need to come together to create a good, high-effort post:
The other thing I tend to do when writing a high-effort post is I actually proofread it before making it. I try to cut out unneeded tangents, reword things that might be confusing, or supplement things that aren't motivated enough.
For me personally, this doesn't take me too long to do since I have been writing and presenting about extremely technical topics for about two decades at this point. Like I mentioned above, informative writing is a skill that gets better with practice. So, doing it regularly as a significant part of my job as well as providing feedback to others on their writing/presentations, has provided me with tons of practice to improve these things.
If you want some formal guidance on scientific writing/presentations specifically, two books I have found informative (mostly on presentations) have been: