That model kind of falls apart for a few reasons: 1. The empty space between the crust and the mantle isn't going to fill up with air. If the mantle cools and

That model kind of falls apart for a few reasons: 1. The empty space between the crust and the mantle isn't going to fill up with air. If the mantle cools and shrinks, it's going to pull the crust inwards because there's nothing to expand to fill a potential void. 2. There's no hard line where the crust becomes mantle. The rock gets gooey in a gradient. 3. If there was a void filled with gas, the gas would desperately want to escape. There's a tremendous amount of pressure down there, and the gas would fart out to the surface as volcanic activity at the first chance it got. Tectonic plates move fast enough that even if such a bubble did form, the gas would escape relatively quickly. But really, consider that if the center of the earth is liquid and cooling, that'll shift the center of gravity in the direction the mantle moves in (same mass, now more dense). That direction is... towards the opposite side of the planet, where there's uncooled liquid mantle, which in turn would just squish back around in time. Cooling the whole mantle evenly around the world enough to decrease the circumference of it such that there's an appreciable void is an unimaginable amount of cooling. As you said, the crust would need to be extremely sturdy, and at that point tectonics would close up those voids pretty quickly.