The reason that you can't is that like all dairy products yogurt is a mix of fats and liquid ingredients with the other liquid ingredients far outweighing the fat content. The reason you can fry with butter is that the production of butter results in the removal of almost all liquid ingredients except for the fat, which solidifies. When you melt the butter, you drive off most of the remaining non-fat liquid leaving you with just the fat, in which you can fry.
Trying to fry in heated yogurt (which will break down) would be like trying to fry in 2 tablespoons of melted butter mixed with 1/2 cup of water. That's probably not the exact ratio but you get the picture.