We can, but it's awkward to do so. By having everything work with powers of 2 you don't need to have everything the same size, but can still pack things in memory efficiently.
If your registers were 48bits long, you can use it to store 6 bytes, or 3 short ints, but only one int with 16-bits going unused. If they are powers of two in size, you can always fit smaller things in them with no wasted space.