"Why do airplanes usually pitch nose-down in a fully-developed stall?"

They don't.

Many GA aircraft are designed in a way that stretches incipient stalls out way longer or that induce incipient stalls much earlier as both options increase the pilots reaction window. Some GA aircraft are designed to induce pitch down during stalls to makes stall recovery much, much easier, but many will only drop the nose to level rather then actually pitch down. GA aircraft that are not designed to stall gracefully tend not to sell very well as they build a reputation for killing their pilots. Commercial aircraft (usually) have stall detection and warning systems so that the situations that could lead to stalls can be avoided. Actually stalling commercial aircraft outside a sim is not something that is done lightly, and as we have seen, the sim behavior often differed from real-world behavior with tragic consequence. Military and specialist aircraft have no rules.

"Why do airplanes usually pitch nose-down in a fully-developed stall?"

They don't.

Many GA aircraft are designed in a way that stretches incipient stalls out way longer or that induce incipient stalls much earlier as both options increase the pilots reaction window. Some GA aircraft are designed to induce pitch down during stalls to makes stall recovery much, much easier, but many will only drop the nose to level rather then actually pitch down. GA aircraft that are not designed to stall gracefully tend not to sell very well as they build a reputation for killing their pilots. Commercial aircraft (usually) have stall detection and warning systems so that the situations that could lead to stalls can be avoided. Actually stalling commercial aircraft outside a sim is not something that is done lightly, and as we have seen, the sim behavior often differed from real-world behavior with tragic consequence. Military and specialist aircraft have no rules.