MangoFang, you didnt mention what type of tree, did you refer only to mango trees? I have seen the "Potassium" only NPK fertilizer requirements only been recommended for mango trees. (The mango tree still requires the minor elements) If someone knows of another tree that this recommendation applies for please let us know.
Also as Jeff mentioned, this is recommended because our soil has enough Nitrogen and Phosphorus for mango trees. But will it apply to other locations? That would depend on your soil.