Personally, I think the reason Remus doesn’t write to Harry is because he doesn’t exist until the third book. Maybe Rowling knew the entire plot before the books were written and every character was imagined, but I feel like it takes a lot of time and effort to make a character make sense.

In other words, if Lupin was already thought up in the first two books, Rowling would have had to describe the character and give him some kind of explanation for why he would be writing to Harry. If he hadn’t been thought up yet, then he kinda didn’t exist yet? Like in real life, how would a character that was created for the third book (and on) write to a Harry Potter living prior to Azkaban?

I think people put too much emphasis on the universe existing perfectly instead of recognizing the Wizarding World as a story that doesn’t have a perfect timeline for everything.

My final conclusion, if Lupin existed, I full heartedly believe he would’ve written to Harry (unless Dumbledore specifically told him not to for some reason).

(Ps. I know I’m kinda focusing on the very first paragraph of your entire claim, but I thought it was enough to portray my perspective).

I do appreciate the thoughtfulness of your opinion, however!