Having spent time pursuing big game for the past 60+ years, I am quite happy to hunt with a true 1.5 moa rifle.
If I am afield with a 1 moa rifle, that merely adds to the confidence.....it is not a prerequisite to a successful hunt.
I have found very accurate hunting loads for most of my rifles,
but that does not encourage me to take low-percentage
shots. [Head or neck] I like the heart lung area, and always try to put my shot into it. With a decent bullet, one can
reach that from even pretty steep angles. I do not take "Texas Heart Shots" unless the animal has been wounded.
My personal choices in these areas has helped me be a very successful hunter, and I cannot ask for much more than that,
except to be allowed to hunt for a while yet.

Dave.