Granted, it's fairly rare that I'm faced with 60' for a first putt, that's more often than not a chip from off the green, but I regularly face 30'-40' putts and through practice and a properly fit putter I expect all misses to be within 2-3 feet at the absolute worst and 18" or less in general. Of course, I can hit an absolute shit putt as well and leave myself 5' short on a 20 footer but those are very much the rare outliers where you say, "aw CRAP!!", the instant you make contact.
My take on this is you're probably using a putter whose weight profile is way off for you and have had to come up with bizarre compensations to get halfway decent results. Experiment with different putters at a shop, or even better, if you have the cash, go see an Edel fitter and have a life altering experience. Your game will thank you.