The simple truth is that we do all that we can to reduce risk of a bad hit, do all that we can to insure a good hit, and then pull the trigger and take our chances -- at any range. The miss factors to overcome increase geometrically as range increases. Fortunately the technology for long range accuracy is phenomenal, but it is not meat in the freezer till we find out if the bullet went where we intended.
I agree with almost all of that but I don't think the risk goes up geometrically with range. The main risks with long range are mis-judging the wind and the animal moving. With good judgment those risks can be minimized by not shooting in tricky winds and not shooting if the animal isn't undisturbed and stationary.
