When I've cropped images on iPad and return to LR desktop, the images have been cropped - but the selected crop factor (e.g. 4:3, 16:9) has not been saved. So when I go in to make refinements to the crop, the crop is not locked to that aspect ratio as it should be.
Ah yes, you are quite right, on closer inspection it DOES sync the ratio, but defaults to unlocked so as soon as I touch the crop it loses the ratio. Locking it when I first open the picture prevents this.
I would still suggest to Adobe that if a crop ratio has been selected on LR Mobile, it should open as locked by default.