Trisodium phosphate is a syngergistic chemical when added to bleach. That and it also is sequestrant, which helps removes calcium deposits, makes the detergent you use a better detergent, aka detergent builder. Emulsifies the dirt and etches the paint to give it a 'profile' for better paint adhesion. I suppose better quality paints are filled with ingredients such as 'Butyl' that sort of melts the previous layer of paint to blend in with the new for a better job. But TSP is just good old fashioned prep - that will make even 'cheaper' paints cling better.