What advantage is gained by having two different words to refer to oneself?
What information is lost if, instead of "I shot the sheriff", me say "Me shot the sheriff" ?
Why does it matter if the speaker is the object or the subject? Why should there be different words?
Likewise "he" / "him", "she" / "her".

Case is pretty vestigial in English. In some other languages it is used more.
I imagine that less-inflected languages, without distinctions of case, must then rely on word-order to convey the relationships between parts. It seems to me that in Latin the sentence parts may appear in almost any order, but English is less so.
How do you feel about genetive case, distinction between “he/him” and “his”? Is information lost between “them spent the evening with his in-laws” vs. “him in-laws”?
hmm innerestin. because ‘his’ automatically implies ownership while ‘him’ doesn’t, it’s tempting to say we need ‘his’. but in context, and getting past the strangeness, ‘him’ as in ‘him in-laws’ could imply ownership just as well.