Equations of state = superfluous state variables?

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Equations of state are essential for describing thermodynamic systems, especially when certain state variables cannot be measured directly. Relying solely on pressure and volume may not be sufficient in scenarios where only temperature is known, as in the case of a thermometer without a manometer. Additionally, phase transitions, such as liquid to gas, require a more comprehensive understanding that includes temperature, pressure, and volume to accurately describe the process. Simplifying state variables could lead to incomplete analyses and hinder the ability to predict system behavior. Therefore, equations of state remain crucial for a complete thermodynamic description.
AcidRainLiTE
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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)?
 
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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?
 
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