You can choose and lock the orientation of the rotate tool by pressing arrow keys or shift before you start a rotate operation. Once the rotate is underway, SketchUp starts looking for inferences of what you want to grab for the rotate and you can’t change your mind about the axis.
But you can always hit escape, and the operation will be canceled with the rotate tool staying focused where you left it. So if you are already rotating and want to change your mind: ESC>arrow key will put you focused in the same spot ready to rotate on a different locked plane.
And has done since at least SU2016, but not in 2014. I no longer have 2015 installed, so can’t check and don’t remember whether this use of the arrow keys came in with v2015 or 2016 - I think the latter but am not sure.
You used to have to get the orientation either from a face, or by click-dragging the protractor tool along an axis, then hold Shift to lock it.
It really helps the SketchUp team if each request has it’s own thread. “Wishlist” type threads are just beyond confusing when more than a couple ideas are discussed and debated. (Ie. this thread should be about improvements only to the RotateTool, and relabeled as such.)