How does substituting yogurt into a cake change the texture and why can it be used?
I am always reminded of a quotation from one of the early episodes of "Two Fat Ladies" the BBC cooking show that yogurt is NOT a substitute for cream. I found that if I needed to address the dietary concerns of a guest, I found it easier to cook recipes that called for yogurt as a base rather than experimenting with an existing recipe that required cream or cheese.

The recipes often depend of the fat content of cream or creamed cheese to provide moisture to your baking etc.

If we are talking about baked deserts, there are a wonderful range of Indian desserts that start with a yogurt dairy base instead of needing cream and milk.

I find that a useful dessert is https://en.wikipedia.org/wiki/Shrikhand