Hi, Joe. TSP is a great grease and oil solvent. Most people do not recognize how oily their walls can become over time from cooking, oily fingers on the walls, smoking residue, etc. Those oils prevent fresh paint from adhering to the old paint. You can use washing products like Soilax or Dirtex which contain a high amount of TSP but have been made friendlier to your hands instead of straight TSP if you wish.
If you are concerned about some strange chemical, don't be. Your clothes are probably washed in a laundry detergent that contains TSP. Many meats are processed with TSP. It is all around you but you rarely see in on labels.