Agreed, almost all... but not all.

I cite for consideration:
- Popeye's Spinach
- Corporal Carrot Ironfoundersson (Terry Pratchett, Discworld), among others with red hair who have that Vegetable moniker
- Veggie Tales
- Bugs Bunny's carrots (especially those with lotsa Iron in 'em, or otherwise made to imbue super powers)