Wouldn't use TSP for laundry, as it is highly caustic and quite harsh on fabrics. In fact my vintage laundry books (circa 1940's) advised women if possible to chose another means of softening water besides TSP (borax, washing soda on the low end, STPP/Calgon,Climatine, and other polyphosphates at the top), as TSP would ruin their hands.
TSP is not even considered a non-parcipating (sp?) water softener like STPP, it forms cloudy water just like washing soda and borax. This means hard water minerals are not sequestered and can end up on one's laundry and washing machine parts.
Using very harsh/alkaline laundry products can lead to a process called encrustation. This is where hard water minerals (mainly calcium) build up on textile fibers rendering them harsh feeling.
Alkaline substances are used in laundry to cause textile fibers to swell, thus releasing dirt/oils. However while swollen, calcium (found in some degree in all water), can enter the fibers and as the fibers return to their normal state, become trapped. This also is what leads to encrustation, and harsh feeling laundry. Sort of what one gets when doing laundry with heavy amounts of washing soda (another highly alkaline substance).
Laundry sours to an extent can remove some of the damage, but many top shelf commercial and even domestic laundry detergents avoid the problem all together by having a neutral pH or slighly acidic. Rather than harsh base chemicals to release soils from textiles, these detergents rely upon high quality surfactants and enzymes. This explains why one is seeing more and more liquid detergents, as they nearly all are pH neutral or acidic, (most rely on citric acid water softeners, and do not contain washing soda, a common substance in all powdered detergents).
Ph neutral detergents, when properly formulated will clean without harming textile fibers and since they are pH neutral, do not require a "sour" final rinse. This is why commercial laundries love liquid detergents as they save money by skipping an extra step. Also certain men's shirts are harmed by aggressive laundry sours. In fact if one reads the care label it will usually state either not to use a laundry sour, or what type should be used.
Powdered detergents can be made pH neutral, but it is a more complex process, reflected in the high cost of these top shelf detergents.
L.