You could slice a cylinder the other way. That would give you rectangles, with the short dimension varying. I'm not so sure you'd save any space, but recycling the unused portion might be more reasonable to do.
The problem is that it is a single crystal of silicon. To keep it atomically flat you cannot cut it at any angle. You must cut it across the axis the crystal grows in or the surface will be rough and the wafer will likely crack in half in a stiff breeze.
I suppose you could go for some more on-axis cuts, but the crystal planes are pretty restrictive on what you can do. You'd end up having super long and narrow pieces and such.
The orientation is determined by the seed crystal. You can choose whatever you want.
There will of course be long and skinny pieces. These will be much easier to recycle than the unused portions around the edge of a circular wafer; they need not leave the facility that cuts the wafers.
The end result is rectangles of a standard size in one dimension and varying side in the other dimension.
The manufacturing process for semiconductors uses a standardized wafer size (in a given fab) so everything can be automated and simplified as far as possible. Having even something like just two wafer sizes makes a lot of the tooling/storage/transfer more complicated and expensive, so it's best to stick to one size and shape.
In order to have uniform rectangular slices of the silicon crystal, you'd have to slice off horizontal cylinder segments. And that would defeat the purpose because if you just used circular wafers you'd have been able to get a couple dies out of that area.
