The reference to ATP is not unwarranted. It illustrates the somewhat unique ability of phosphate compounds to store and release energy.
The action of STPP or sodium tripolyphosphate, the compound most commonly found in phosphated laundry products, is also energy related. Its ability to bind and hold in solution hard water minerals, and similar mineral-laden soils, is due in large part to the fact that the STPP molecule has stored energy. That energy is used to bind the minerals and keep them away from fabrics, and it also helps the molecule stay in solution so that the entire package can be rinsed away.
The high energy state of STPP also helps to explain why it has a limited shelf life. Over time, in the presence of moisture and heat, it will spontaneously decompose to a lower energy state, similar if not identical to its cousing, TSP. TSP also binds minerals, but due to its simpler structure it cannot keep them in solution, and will deposit itself and the minerals as a precipitate on fabrics and washer parts. Washing soda has a similar issue.
The ability of STPP to bind and hold in solution such minerals is just one part of its usefulness in laundry. It also serves the following washing functions:
1) As a "break", literlly, breaking soil away from fabrics
2) As an alkalinizer, lowers the pH of the wash water so that fats, oils, and greases are more readily converted into substance that are released from fabric and rinsed away. This is a process similar to that used to make soap from fats: saponification.
3) As a water softener. Although this is implicit in the preceding discussion, it's important enough to list separately here.
All together, there is literally no other chemical compound that equals the three-fold power of STPP to get laundry cleaner. Due to the restrictions on phosphate use in many areas, laundry mfgs have spent a lot to come up with substitutes - but typically it requires a rather complex cocktail of chemicals to even approach the effectiveness of STPP.
As for the environmental concerns, this is a somewhat controversial topic, and one which is largely mimsunderstood by the general public. I won't go into more detail here, other than to say that geography, climate, and wastewater handling systems are determining factors in whether or not phosphates used in laundry are really an environmental problem at all. I would also add that the average human body dumps more phosphate down the drain than regular use of a 30% STPP laundry detergent would. This is because phosphate is an essential nutrient - without it our DNA would collapse, we would have no energy to do anything, and we'd die rather rapidly.
