My point is at <1" I'm sorted, that's enough for me and I get out and use them, no doubt by changing bullets, powder, seating depth etc. I could halve that in most of my rifle but I don't think I'd miss less or kill more.
As for the deer point, this is why most people chest shoot deer rather than head shoot - on a roe your 'kill zone' is 4" granted but if your POA is correct then too low for the heart and its generally a clean miss, 2" high you are top of lungs / spine resulting in dead or immobiled deer, 2" too far forward you break both shoulders / hit the Hilar zone resulting in a dead or immobile deer, 2" too far back you hit the liver, deer will run but you should have a good blood trail and deer should bleed out quickly so humane (only time this has happened to me deer didn't make 100 yards).
Also with 4" kill zone as mentioned above you are talking roe, as the species get bigger so does the kill zone, about 8" on a red . . . . I've also seen Kenny hit 8 bulls in a row with a 7.5 x 55 and iron sights, rested off of a bag, at 900 yards and he usually shoots from a high seat on deer.