Leaving the pin in may change these numbers a bit, but here is some great research on "putting capture speed" . . . which clearly shows that the further past the hole your putt would have gone, the less margin for error you have to sink it.
Those numbers get a bit larger at stimp 12, of course, because what really matters is the speed of the ball at the hole. People have a hard time visualizing that, though, so the "effective width" of the hole is a reasonable way to show it to people.
(I would assume you know all of that, though, so I'm just repeating it on the off chance someone else here hadn't thought of it much.)
Dying the ball into the hole is still the way to go. Just don't leave it short.
FWIW, inside of 12' or so, we advise amateurs not to leave any putts short, and outside of 25' or so we advise them to hit the putt the exact distance of the hole.
Amateurs leave far too many short putts short, and the few more putts you leave short on the longer ones will more than offset the ones you hit well past the hole and three-putt.
Here are some more stats from the PGA Tour:
In 2018, ~11,000 putts hit from 10'+ traveled 4'+ past the hole.
That doesn't count putts that lipped out and sat closer to the hole than 4', or putts that lipped out and went left or right. It only counts the number of putts on the PGA Tour in 2018 that were hit from 10'+ away and which finished
behind the hole by 4'+.
That's a LOT of putts that could be affected by the flagstick being in. (Only a percentage of them will have contacted the flagstick, but given that pros miss high and low about 50% of the time… the distribution favors the middle… minus those that go in the hole, but those aren't counted in this 11,000 figure as they didn't go "past the hole.")