This site provides a lot of information.
http://www.canr.msu.edu/vanburen/e-896.htm
N-P-K always given in that proper order.
In part---from the web site, "Most phosphate fertilizers are highly water soluble. Phosphate water solubility is very important for early plant growth. Thus, it is important for banded starter fertilizers to contain highly soluble forms of P"---
I tend to think of it being needed for plants that produce fruit, i.e. a crop you harvest that is not a part of the plant itself like a beet would be. Pods, watermelon, wheat, etc.
Nitrogen for growth as you said.
Personally I generally combine two formulations of dry fertilizer, but one should really get soil tests done and feed accordingly.
I am also a believer in micronutrients. When still wheat farming soil tests showed that I needed to apply iron and zinc. Did apply both and believe it made a difference. Costly to apply, and stinky. Used liquid.