What specific properties of CFGs & CSGs do we lose, when we redefine the starting symbol to be either terminal or non-terminal?

Question

Both CFG(Context-Free Grammar) & CSG(Context-Sensitive Grammar) are defined as a 4-tuple $(V,\Sigma,R,S)$, with $S\in V$.

That is, in both cases $S$(the starting symbol) is a non-terminal symbol, why is that the case?
What properties do we lose going from $S\in V$ to $S\in V\cup\Sigma$?

e.g, is there a property that doesn't extend to $(,\{a\},,a)$?