As someone who use to line up putts with a line. There are a few issues.
First, the putters eyes might not be over the ball. So if the line is vertical, and you are now looking at the inside half of the ball, the line looks off. Trying to line up the ball with the line on an angle is just counter productive.
Second, greens are not perfect and sometimes its very hard to get the ball now to roll half a degree or so. This can make lining up very tedious.
Third, this is horrible for a perfectionist because they might take forever trying to line up the ball.
Fourth, it might throw off alignment. I learned from my Edel fitting that lines on the putter can effect how you aim. With out two lines on my putter I aimed way right. Draw two lines, about a ball width apart, and I can aim straight. Now add another line, and it might throw off how you align your putter behind the ball. This also can defeat the purpose.
I just think there is a long list of things that caused me to stop doing this. I prefer not to look at anything on the ball while putting. I rather trust my putter and my ability to aim it. If someone has trouble aiming the putter, then go get a putter you can aim.