Woodoworkery:
I think that maybe how hard you hit the putt may have a lot to do with it. just enough to get to the hole may let the break ,break more. A little harder and the putt may hold the line a little longer before it breaks, and not make the break that much very very tricky.
That's indeed what makes putting quite hard, you have two variables: aim + power. So there are several combinations which work. (Don't forget also that in all these 3 videos, the greens are very fast, not tourney. So I used a bit less break and hit harder).
The safest way to putt is such as the ball will die in the cup because you avoid many lipout. But then you take the risk to get short putts once in a while (and a short putt is always a missed putt) and you need to move the aim more to counter the break. The more you move the aim the more you get errors. Indeed, even if you are accurate and can move the aim with, let says, 10% accuracy, if you have to move the aim a lot, these 10% will represent a distance larger than the size of the cup and you have more chance to miss.
So in my view, the best is to set a power such as if you miss the putt, the ball will stop at 3-4ft behind the cup. Like this, first of all, you fix one variable (power), you are thus left with the aiming variable only, secondly, you avoid short putt, thirdly you need to move less the aim reducing the possible errors and finally such a power is still reasonable to avoid too many lipout (still they happen).
Of course, putting is pure feeling and practicing is the key. On one day we are putting great, on the other day that's another story.
Regards