Your post contradicts itself. You say all they care about is winning and that is correct. That’s why they are shifting the offensive duties away from Garrett. Then you say they have emotional capital vested in Garrett even thoug his offensive systems haven’t been successful. If Moore shows significant improvement in the offense then the GM will have to say hands off Moore to Garrett. How will the emotional capital hold up if Garrett takes a position he is going to get involved with the offense again?
No, that's not what my post said. I asked an either/or question: do they care more about winning, or about Garrett succeeding because they have "emotional capital" invested in him? There's ample evidence that Jerry values Garrett's role as HC not only because of the emotional capital -- Garrett is like a surrogate member of the family -- but also because Garrett is willing to absorb regular doses of humiliation from Jerry.
And during his 8 1/2-year tenure, Garrett's "offensive systems" have produced exactly three post-season appearances and two playoff wins. That kind of record has been mediocre enough to get more than a few coaches fired. It hardly qualifies as "successful."
Garrett can't control Jerry, but he can control how much influence or visibility his coaches have, especially on the offensive side of the ball. Garrett wins just enough to keep Jerry from becoming "irrelevant," which Jerry dreads more than anything, and does so at a comfort level that lets Jerry relax.
If Jerry were to fire Garrett after all this time, it would immediately raise question of "what took so long?" And though Jerry says and does profoundly stupid things all the time, firing Garrett at this late stage would finally expose his incompetence for what it truly is -- the underlying cause of 25 years worth of futility. Jerry fears looking stupid almost as much as he fears becoming irrelevant.