Can't say I agree with you about missing a downhill putt from 3 foot and the ball is still on the green ...
If your 3 foot putt was originally for Par, you take unplayable, you are making next putt for Double Bogey ... with the mental image on your ball rolling 10+ feet past the hole in your mind ... that's a really tough thing to deal with mentally
If you choose to play where it lies ... 2 putts uphill from 10+ feet should be given, and you still have a chance for a bogey if you make the putt ...
Of course if you putt off the green into a collection area and have to get up and down for double, then I would completely agree that taking the unplayable and replaying the first shot is a much better idea
What's in the Bag
Driver: Callway X-Hot 10.5 with Fubuki 50S (pulled from a TM Burner SuperFast)
Woods: 19 Deg Callaway X-hot Proj X Stock S Flex
Hybrid: 22 Deg TM SF i70R, Cobra Baffler 25 Deg NS950R
Irons 5-Pw: Titleist 704 CB NSP950 (Flex Unknown - think it is R)
Wedges: Perry Gear 52 Deg DG S300 and BFG 55 Deg KBS Hi-Rev, Tourstage 60 Deg
Putter: RIFE Antigua Island with Champ Large Grip