Let’s say each block depends on 1,000 blocks from before, but which 1,000 blocks those are depends on which block it is. If consecutive blocks don’t share many or any of the blocks that they depend on then any sufficiently long series of blocks will require all of the previous blocks to exist. Recomputing them on they fly would become prohibitively costly.
And that is the point. It’s not important to make cheating impossible, it’s enough if it’s cheaper to actually have the claimed amount of free space than to lie about it..
The seed for the algorithm would depend on the section ID so that section members can verify each other. This makes this kind of cheating impossible unless one can place two or more vaults in the same section.