Equations of state = superfluous state variables?

[AcidRainLiTE]

I don't get the point of equations of state since they seem to me to just indicate that we defined too many state variables. Why not just trim down our set of state variables and do away with the equations of state (i.e. for an ideal gas, just notice that P and V are sufficient to describe the system)?

 

[DrClaude]

But what if you can't measure P and V? What if you know the volume of a vessel and you have a thermometer, but no manometer. How are you to work with that if you don't have an equation of state?

And what about processes that take place at constant T, like phase changes? Do you really want to describe the liquid -> gas transition only in terms of P and V?