Eyedropper tool picks up and applies object size: height, width, or both.
I am constantly resizing vector objects to fit over clipped images, to make Spot UV objects, and it would be great if I could just eyedropper the image, rather than opening transform, copying, clicking the shape, pasting. Seems simple until you do it a lot. Adding this to eyedropper seems simpler.
Miles, the shape size changes with each new panel & project, so recording an action wouldn't be practical.
I just posted a similar suggestion before I saw this. Another way it could work is similar to the Align tool. You could match width or height to a key object.
Miles Stevens commented
Great idea! In the interim, I'd record a few actions with the dimensions you like, click the hamburger icon in the Actions panel, and select "button mode" for quick execution. Might even be easier than your eyedropper idea.