There are a few situations where making a distinction can eliminate a syntactic ambiguity, as in "its fun"/"it's fun". There are also a few more where it eliminates a non-ambiguous but awkward construction, as in "it's its own server". And of course it'd introduce another kind of irregularity unless you got rid of the contraction apostrophe altogether, which might lead to some other strangeness that I haven't thought of yet.