The reason is that "it's" is only a contraction. The entire purpose of "it's" is to represent "it is" or "it has." You could think of it as the written recognition of common slurring between those two words, though there is more to forming contractions than just that.
Possessive pronouns have been acknowledged for far longer and none of them use an apostrophe. Ever. So, at the very least, the apostrophe is used to make a strict grammar distinction and to indicate that "it's" is still meant to be two words.
Yu-he-heh!!!BOINGBOINGTake this, take this!!!Uu......
Papa, Mama......Even though it's impossible to take it easy with a sword like this, myon...Sorry, myon......Yuwaan!!! Hurting meee!!!These country bumpkins!!!Reimirya and Remirya are noisy!Mukyakya! Serves you right!will be punished, ze!!!Cirno that can't take it easyYukkuri Theatre
Cirno's love
melody ①
check those tiny kanji