You probably know that a horizontal flip followed by a vertical flip is the same as a rotation by 180°, and i often use that.
If the transformation palette had a diagonal flip (along the x=y diagonal, going through whatever centre point has been selected), then you could also rotate by 90° without using the rotation tool, by using a suitable combination of flips.
It fact it would then be possible to do all flips and rotations of the square (generating the Dihedral group on the 4-gon: Dihedral group - Wikipedia).
The icon would look something like this:
