How do valve deformities limit cardiac function?

It depends on what valves you're talking about, but they lead to similar pathology.

If we're talking about the heart valves, malformation of the valves will surely lead to blood flowing in the both ways. The heart valves are responsible for the unidirectional flow of blood in the heart. If they are affected, the arterial ( O2 ) blood will mix with the venous ( CO2 ) blood. Sure, the body still receives oxygen and eliberates carbon dioxide, BUT:

• Both carbon dioxide and oxygen are important for the respiration process. The exchange between the gases occurs through diffusion, which means the flow of a substance from high concentration to low concentration ( in order to estabilish equilibrum, as most of the body functions do ). That means if the erytrocytes don't have a big concentration difference between the two gases inside them and the air in the alveoli, the diffusion will have a lower gas exchange rate or won't happen at all.

• Because what i said in the above paragraph, some sensors of CO2/O2 levels will determine the heart to beat faster, which everyone knows is a bad thing if it is a habit for the body.

If it's the venous valves that malfunction, it will make the blood flow more difficult and sooner or later you will have some severe heart diseases due to high arterial pressure and/or tahicardya.

So, overall, valve deformitites affect the whole organism because they affect the oxygen-carbon dioxide exchange. Given that, if the heart receives less oxygen, its cardiac muscle cells will eventually begin to die and cause a heart attack.