I've always wondered why を can not be used with existence verbs(いる、ある、おる、なる、生きる【いきる】、死ぬ【しぬ】. They're all intransitive verbs but is there a legitimate reason? Is existence "indirect"?
There's a difference between intransitive and indirect. Transitivity (from Latin "transire", "to go across") basically (with exceptions, probably) implies the subject carrying out an action on an object that is generally distinct from the subject. Sure, you can select 自分 as the object to make the action reflexive, but in general you are able to select objects that are not the same as the subject.
Verbs such as いる and ある have no transitivity, or "going across" from subject to object. Neither do the English equivalents.
〇「家にいる」= "I am staying in the house."
✕「家をいる」= "I am staying the house."
In the second, I translated the accusative 「家を」 as the accusative "the house", and both were nonsensical for the same reason.
Putting the subject of basic existence verbs as the object likewise makes for odd translations:
「私を生きる」= "[It] lives me"
「彼を死ぬ」= "[It] dies him"
(Note that anything marked with を in Japanese typically must go after the verb in English, because of our Subject-Verb-Object [SVO] order .)
So, this isn't just a feature of Japanese, but also of English. Now, in colloquial English, we're allowed to say things like "it's me" in place of "it is I". This is suppressed in formal English because it's an unusual feature of our language that rubs grammar purists the wrong way. We can also say "I am home" instead of "I am at my home"; this is an unusual case called the "locative"*, and it only happens with a few words in English. For example, we can't say "I am store"!
*Actually, that's what it's called in Latin, which has the similar phenomenon on a larger scale. I don't know if the phenomenon in English has a name. Latin, incidentally, marks objects and subjects very similarly to Japanese, and has the same intransitivity in existence verbs.