Why does a cake that puffs up in the oven sink as it cools?

Answer: The cake's inside has not set into a firm structure before it cools.

Too much steam escapes from the oven, so the risen bubbles lose their support. — Steam helps the batter expand, but it is not the lasting support that keeps a cooled cake up. The real support is the set structure around the bubbles; once that structure is firm, escaping vapor matters much less. More steam would not finish the structure and could even make the cake more fragile.

The center is still too wet and needs more drying to hold its shape. — An under-set center can feel wet, so this explanation gets close to a real clue. But good cake crumb stays moist and holds its shape because starch and proteins have set around the bubbles, not because the middle has been dried out. Drying the center further would not build the missing structure.

The cake's inside has not set into a firm structure before it cools. ✓ — During baking, heat gelatinizes starch and coagulates egg or gluten proteins, building walls around the gas bubbles. If cooling starts before those walls are firm, the trapped gases contract and the weak bubbles collapse. A cake can look fully risen at its peak and still sink minutes later because expansion outran structure.