I have seen protein suggestions based on all kind of factors: body weight, lean body weight or lean body weight modified by muscle mass.
The only one of those you can reliably measure is body weight. Body fat measurements are not really accurate and as a result you'd get an inaccurate lean body weight number. Same goes for determining the muscle mass.
On top of that body shapes vary. There are people with longer or bigger muscles and people that have thinner or smaller ones. Some people are just more bulky than others depending on their genes.
How the protein metabolism works isn't completely understood, too.
And lastly not every protein source is as valuable as the other. What counts are the amino acids that make up the different types of protein. There are some types with a high value protein profile and some with lesser value. A combination of two proteins with a low value protein profile can however result in a high value profile, just because the proportions of essential amino acids evened each other out.
It would be really complex to put all those factors into a formula to calculate a specific result. Still that formula wouldn't be very accurate. It is easier and saves you a lot of time to make some assumptions on most of these variables and only use the number with the highest effect - body weight - to calculate your protein needs.
In fact the 2g/kg are the maximum that can effectively be used in muscle protein synthesis. Everything above that value isn't necessarily going to waste, but probably just converted to energy.
So instead of recommending you something that might be insufficient, Starting Strength just goes with the maximum as their simple estimation to be on the safe side. Unless you have kidney problems, a balanced diet high in protein is safe.