Why the view "I am the owner of my karma" not contradict anatta? Why did the Buddha advise lay people and monks to think, "I am the owner of my kamma, the heir of my kamma; I have kamma as my origin, kamma as my relative, kamma as my resort; I will be the heir of whatever kamma, good or bad, that I do" when this seems to contradict anatta?

Isn't thinking "I am X" contradicting the teaching of anatta?

There are suttas where the Buddha advised not to associate the five aggregates with the self e.g. SN 22.93. Aren't these two teachings contradictory? Isn't "owner of kamma, heir of kamma" a mental fabrication (sankhara) that we shouldn't associate our self with?

Why didn't the Buddha advise lay people and monks to think, "there's no self in this body and mind doing anything"? What's the consequence of this view? 

From AN 5.57:


  “And for the sake of what benefit should a woman or a man, a
  householder or one gone forth, often reflect thus: ‘I am the owner of
  my kamma, the heir of my kamma; I have kamma as my origin, kamma as my
  relative, kamma as my resort; I will be the heir of whatever kamma,
  good or bad, that I do’? People engage in misconduct by body, speech,
  and mind. But when one often reflects upon this theme, such misconduct
  is either completely abandoned or diminished.
This is how you practice equanimity (upekkha). It's the one of the four divine abodes. Just like in Metta(loving-kindness) meditation where you say "may I/my parents/relatives/friends be happy, well, free from suffering etc.", Upekkha meditation is also practiced at a conceptual level. 

The purpose of Upekkha meditation is to cultivate equanimity in the mind. It does not lead to realization of Anatta nor enlightenment unless you turn it into Vipassana at some point.

Anatta is at the level of ultimate reality. That is for advanced practitioners of Buddhism. Trying to teach Anatta to everyone regardless of their mental maturity will not be productive as many will endup being more confused than they already are. That's why there are teachings in Buddhism that help you develop the mind at a conceptual level where you are familiar and comfortable. It is important not to mix up these teachings with the teachings of ultimate reality.