Actually I think Potato isn't a piece of flesh from Zombies, just what they had stolen from a village. Like Polar Bear, It drops Raw Cod rather than cooked one when a burning bear dies since Polar Bears are not fish and they just catch them for food. When you kill a bear you will get its food. So I think dropping Baked Potato from a burning Zombie is unreasonable.
Linked issues
duplicates 1
Comments 4
Duplicate of MC-231505, which was later resolved as "Works As Intended".
Polar bears do drop cooked cod when burning (MC-102269). As @unknown stated this is intended behavior.
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In the case of the polar bear, it's cold. So it probably makes more sense for its food to drop raw even if it was burning. However zombies aren't cold. I'd say the zombie being on fire would warm the potato up quite a bit, would you?