I don't think you would choose to use this particular sentence in a serious communication with anyone. The letter case would just not be enough of a distinguishing factor for you to risk the wrong meaning being conveyed. The letter case only has a very small meaning once you get used to using small caps.
All languages change and have ambiguities. Modern English (with Capital Letters) has lots of ambiguities that cannot be disambiguated with capitals (e.g. "a small girls school")
Conversely, on its own, the fact that they remove some ambiguities is not a sufficient reason to use them.
Since the downvoters disagree, I'll provide a proof.
1. Suppose resolution of ambiguities is a sufficient reason for a separate case in written language.
2. Ambiguities exist that are not resolved.
3. New cases are not created to resolve these.
4. By contradiction, 1 is false.
QED
There may be other reasons which in addition to the resolution of ambiguity are sufficient to justify case, but you can't simply cite the resolution of ambiguity and say conclude that case is justified.
to add - the main meaning of upper case is to help separate sentences, because the dot alone is not enough, unless the reader is specifically used for the dot to be the only separator. this is an example.
I had to help my uncle Jack off a horse.
i had to help my uncle jack off a horse.