> Why not just have the value be the base 2 logarithm of the page size, i.e. a value between 9 and 16?

Yes, that would have been a better choice. Originally, the file format only supported page sizes between 512 and 32768, though, and so it just seemed natural to stuff the actual number into a 2-byte integer. The 65536 page size capability was added years later (at the request of a client) and so I had to implement the 65536 page size in a backwards compatible way. The design is not ideal for human readability, but there are no performance issues nor unreasonable code complications.

The page size value is not the only oddity. There other details in the file format that could have been done better. But with trillions of databases in circulation, it seems best to leave these minor quirks as they are rather than to try to create a new, more perfect, but also incompatible format.