For what it's worth, his, her and its as possessives come from similar constructions and do not take the apostrophe. This is useful, of course, because it leaves it's free to be a contraction of it is.

Now here's where I run out of firm-ish knowledge and enter areas of discussion where I may be like the blind leading the blind, but that has never stopped me before. :

The original apostrophe for possession was also a contraction - in the earlier case, of John his table, say, becoming John's table. And so on. In that sense, the only possessives in the language are his, her/hers, its and their/theirs. All others may be considered long-forgotten contractions of these - hence the apostrophes.

Come on you ayleurs, awadians, wordsmiths and others - correct me...