There is no such word as "its". That archaic usage was an exception to the "appostrophe-s" construction used to indicate possession. Deprecating that usage eliminates that unnecessary rule exception. While abandoning this antiquated rule does create a homonym, the contractive or possessive meaning is clear in context, as your criticism clearly demonstrates.
"It's" is both the contractive form of "it is/was" and the possessive form of "it".
Only English teachers and similar obnoxious, gatekeeping pedants mourn the loss of "its".
I think you should actually read your link:
The "its" construction espoused by Messrs. Merriam, Merriam, and Webster was a satirical attempt at formalizing an exception to the possessive rule rather than acknowledging a typographical error in an advertisement for their new dictionary. That satire was lost on the general public, and "its" was born.
Your commitment to their 250-year-old joke is laudable, but the joke itself has run its course. "Its" was never actually a word. It was always a typo.