Agreed. The possessive and contractions should be homonyms, both carrying the apostrophe. “Its” would be the nonsensical plural form of an inherently singular word: “This “it”, that “it”, and those “its” over there…”.

The good news is that all words are made up. We can, indeed, use the same “it’s” for both the possessive form of “it” and the contraction of “it is”.