I hear there’s an excellent attorney in that family…
Why pumpkin or sweet potato pie? It’s the sweetness and (IMHO) that cool orange color.
I don’t know how carrots compare in terms of actual sugar content, but as veggies go, they taste quite sweet to me.
Not a dumb question at all. It was only late in life that I learned that carrot cake (which I adore) contains actual carrots (which I detest). I had always assumed it was just a name. You know, like Grape Nuts.
What else would you want to call a cake made with carrots? Apple cake?
By law, carrot cakes must have a depiction of a carrot on them. Naturally the inverse is also true. So to answer the OP, the purpose of putting carrots in the cake is to provide legal justification to having a depiction of a carrot on the cake
The only purpose of carrots in carrot cake is to allow oneself the delusion that you can eat more because it contains vegetables. Unfortunately, nobody will buy it when you tell them chocolate is a vegetable. Luckily, carrot cake is also delicious.
Wow. psychobunny likes carrot cake.
Alert the media.
When they are cooked, they are rather sweet. Raw, though, not really. There’s a vague sense of sweetness, I guess, compared to similar vegetables, but nothing like the other sweet veggies.
Though carrot juice is sweeter, too. I’m not sure why that is. It’s that same flavor you can taste in carrot cake. (Which is why I didn’t ask this question.)
I made the cranberry-sweet potato muffins found onthis CBC page. The muffin interiors would not set, after half an hour I covered with foil and turned down the heat and cooked for another 10 minutes. They ended up like an old fashioned pudding or some sort. Edible but only by me. 
I followed the recipe exactly, exept i had fresh cranberries that I boiled in apple juice then drained off the liquid. Was that what left them under cooked inside? I generally do not use substitutions on the first time I make something, so all the rest was as written. I used cold roasted sweet potatoes that I mashed up to make the required amount of sweet potato.
They tasted yummy but the texture definitely left something to be desired. 
They were very much like a cake that had fallen, but to fall you first have to rise.
I have made zucchini cake, zucchini cookies, and zucchini quiche, among other zucchini things. (No, I don’t plant them anymore.) Oh, zucchini bread, of course.
They all came out pretty good. The cookies tasted like ginger snaps.
We made a carrot cake from this recipe this week. It’s, hmm, OK. Nice toasted with butter.
I’ve looked at that recipe too. It’s a healthier carrot cake. More like a coffee cake or sweet bread than a sweet desert. The lady mentioned putting a slice in the toaster. We’d probably just eat it buttered and omit the cream cheese frosting. Seems perfect for a breakfast or a snack with coffee.
People eat zucchini cake all the time, only they usually call it zucchini bread, just like banana cake is usually called banana bread.
And squash pudding is delicious, it’s just pumpkin pie without the crust. Unless you mean zucchini/summer squash pudding which doesn’t sound so good. But winter squashes would make excellent pudding.