What are bologna and hotdogs really made of?
I doubt you will find a specific ingredient list that identifies particular cuts or parts of meat.

As an example, here is the ingredients for Oscar Mayer bologna: Mechanically Separated Chicken, Pork, Water, Corn Syrup, Contains Less Than 2% of Salt, Sodium Lactate, Flavor, Sodium Phosphates, Autolyzed Yeast, Sodium Diacetate, Sodium Ascorbate, Sodium Nitrite, Dextrose, Extractives of Paprika, Potassium Phosphate, Sugar, Potassium Chloride.

Similarly, you can probably look up the ingredient lists for other brands and products.

Making an emulsified sausage (hot dogs, kielbasa, bologna, mortadella, etc.) from scratch is not that difficult.  You would probably not want to make it exactly like these companies do.  They are mass producing and need to ensure shelf life, as well as safety.  There are a lot of things on that ingredient list above, for example, that you would not need if making this at home. Additionally, these companies weigh quality against cost efficiency.  At home, you would likely use higher quality ingredients.  Although, there is an argument to be made about the parts of the animal that are desirable vs. not.  This could just be your preference.  I'm not sure how you are defining "premium."  I assume that in general, the parts of the pig, cow, and chicken, that can be sold at higher prices are not used to create emulsified sausages.

In the end, you probably get what you pay for in terms of quality.