Well, for a period of time in "middle english", it was spelled "whos". Ultimately derived from the genitive singular form of Old English hwa, "hwaes". In OE the -es suffix marked the genitive case in strong masculine nouns.
Eventually, the form become generalized across all nouns, with -es being applied to any noun to indicate possession. In most cases, the e is silent, and typographers began to either omit it (e.g. "whos") or, eventually, replaced it with an apostrophe, as the French did. And I suppose "whose" gained an e to indicate the "long vowel".
So we've ended up in a situation where we've basically lost noun declension and just attach suffixes to indicate plurality and possession (s and 's), but our pronouns have inherited their old declensions, without the -es/-'s suffix attached.
Granted, "its" is itself a semi-recent invention, as OE and middle english used "his" for both masculine and neuter third person singular genitive pronouns.