One of the problems to using the line on the ball is that player's react to it with their strokes. Let's use Tiger Wood's stroke as an example. Tiger opens the putter more than average on his back swing. A perfect arc is about 4 degrees open to 4 degrees closed (Iron Archie robot. Tiger uses about twice that much. So right at impact you see this hit or rapid closing of the putter at impact. For Tiger that brings the putter to a closed position realtive to his path. So his best strokes are a little inside out.
Some players using a line have straighter paths with less rotation. But the same release!! Closing the putter more and hitting pulls. We thought that release was a reaction to the line. After about 6 months of tests I can say with some confidence that it was. For every player I worked with who used a line I asked them to hit some putts without one. The release changed and slowed dramatically. For some the problem was amplified because once they hit a couple of pulls they began to steer or search with every stroke and lost their consistency.
This is not a knock on using the line!! Only an example of how some can't use it. There are many players who use the line successfully. Anything is possible with some knowledge.