Cooking: To Peel or Not to Peel Veggie Skins?

Should we or shouldn't we peel veggie skins like those of carrots and potatoes before cooking?

This is an ongoing source of humorous disagreement between my wife and me! She peels the skins off of things like carrots and potatoes almost always before cooking. Yet I like to keep the skins on and just scrub and wash them and maybe cut away any dirty-looking parts if I'm making things like a roast or french fries or anything of this sort. She thinks it's rather amateurish to keep the skin on.

My ultimate rationale for keeping the skins on is that I'm lazy! Yet I also enjoy the skin and the sort of rustic feeling it adds to our cooking. To my understanding, the skin also often contains the most nutrients, especially with potatoes. So why not keep the skin?

For the experienced cooks out there, what do you do, and is it case-by-case? What's your rationale?
Cooking: To Peel or Not to Peel Veggie Skins?
Post Opinion