The watch thing: curved faces are more liable to scratches but less liable to fracture - the force of the impact is deflected sideways and so doesn't smash the watch face. See the design of mediaeval armour, which deflects spear points away from vital organs.

It looks to me like they thought they had a material scratch-resistant enough to make it worthwhile moving to curved faces, and then found they didn't.

I suspect the jar thing is also explicable in that the convex undersurface makes a better airtight seal stopping the coffee going off. As far as spillage goes, instead of holding the lid under the spoon while transferring to the cup, why not hold the cup under the spoon?