Why do we even have $\subseteq$? [closed]
With $\subset$, a reader might not be immediately able to tell if it is referring to a not-necessarily-proper subset (i.e., $\subseteq$) or a proper subset (i.e., $\subsetneq$). After all, different authors use $\subset$ differently.
On the other hand, the notations $\subseteq$ and $\subsetneq$ only have one meaning, so these notations immediately remove any ambiguity.