It seems like there is a usual practice of saying a psalm or a fragment of a psalm before starting into a set of blessings. I have been taught that this is to mentally prepare yourself before the main prayer service starts. Some examples would be Ashrei before Minchah (and Selichot?), V'hu Rachum before Ma'ariv, and maybe Psalm 30 before Baruch She'amar or in an expanded view the whole of P'sukei d'Zimra before Shacharit.
With this as background, it seems notable that before the morning blessings, therefore before the main public service the way we do things today in Ashkenazi custom, there is no psalm. People say Modeh Ani earlier and perhaps Ma Tovu and some Torah or Talmud verses after the early morning Torah blessing as personal preparation, but I don't remember seeing a psalm in this section in any siddurim.
I don't know if this was ever a conscious choice on the part of any rabbis or if the practice just happened to evolve this way, but the difference is notable and perhaps someone has written on the topic. Does any one try to explain why there is customarily no psalm early in the morning?