Why does calculating formal charges help us draw correct Lewis structures?
Formal charges are helpful for two reasons:

at lower levels, you use them to show your instructor that you can properly count electrons and ‘keep the books’. You would need to realise that each oxygen has an additional electron and therefore a formal negative charge while sulfur is lacking two electrons and therefore has a formal positive charge. Adding up the formal charges should give the charge of the molecule.
Since all lone pairs are typically drawn at this level, lacking formal charges can easily be rederived.

at higher levels, lone pairs are typically not drawn unless they are important for some reason (e.g. if they take part in a resonance mechanism discussed at this very moment). Therefore, the only information on the number of electrons around an atom we can extract from the formula is the formal charge.
If at higher levels, you draw a tetravalent sulfur atom without formal charges, we must assume that it is actually a formally neutral sulfur and that there is an additional lone pair. This, of course, makes a big difference; compare the electronic states of sulfur in $\ce{SO4^2-}$ and $\ce{SF4}$.