Why dont potatoes show they were once attached to a plant?

The potato doctor removed the placenta very skillfully.

They do, you're just not looking close enough.

They have a small protrusion at one end, about 2mm across, usually ever so slightly rough. That's where the stolon was attached. You're probably just mistaking it for another eye, as you don't know what to look for. 

Contrary to what the other person said, the eyes of a potato are not where the potato was attached to the plant. Rather, the eyes are where new shoots will grow should the potato be planted. 

The 'eyes' show that they were once attatched to the plant roots.

Potatoes are a plant. Plant one at the appropriate time and you will see this to be true. 

Probably Meagan Markle