More putts are missed because you are off-balance than off-line. We have all had that experience of "not feeling right" while standing over a putt whether that putt was from 40 feet or a tap-in. And "not feeling right" is better explained as not being in balance.
One of the first contributors to good balance is the position of your head. This 15-pound computer stacked on your shoulders can cause a variety of balance issues not the least of which is falling over.
So if subconsciously you are more concerned with balance (not falling over) than with your line, you'll experience more miss hits than solid putts.
I am not talking about literally falling over; I am saying that the computer stacked on your shoulders is a very sophisticated device that recognizes when you are out of balance and will seek balance to the detriment of keeping that six footer on line.
Stabilizing your body posture also has a lot to do with keeping your head in the right spot while bent over trying to hit putts. The older readers remember Arnold Palmer's knock- kneed and pigeon-toed address which really stabilized everything so that all he had to do was pop the ball on line. In his prime he was amazing.
Jack Nicklaus crouched over his putts but, more importantly, tried to get his head in position so that he could see the line better and up until Tiger Woods, Jack was regarded as the best pressure putter ever. When another old timer, Sam Snead, went to putting with the putter between his legs, which was banned by the UGSA, he had optimum vision and I would argue that he had better balance.
If you have tried putting with your eyes closed, you think you are eliminating your tendency to "yip" the ball and you would be partially right. But you are more effective simply because you are getting yourself in balance first. When you close your eyes, you immediately seek balance to keep from falling. And once you are in balance it is much easier to stroke the ball.
How do you get in balance? Stand over the putt the way you normally do. Then forget about the putt and ask yourself, "Am I in balance?" If you don't feel that you could move your arms with total body balance, stop! Reposition your feet until you are in complete balance regardless of where your feet end up.
Not everyone can be square to the line like Woods; Nicklaus wasn't and he did just fine.
Work to balance and then stroke the ball on line. You may find it much easier once you are no longer losing your balance.