I go through phases between using the line on the ball or just picking an intermediate target. I went for 2-3 years without ever using the line because it distracted the heck out of me. But now, I do use the line, so go figure. My guess is over time I have figured out a way to use the line to my advantage.
The basic routine is:
1) get a quick 1st impression read (aimpoint assisted to varying extents)
2) aim the line on the golf ball on my intended start line
3) step six or seven feet behind the ball and check the line, as I tend to have a much better perspective of things from this vantage point. I also tend to make 1 or 2 practice strokes just looking at the line and hole from here (stole this from Fil).
4) go back and make adjustments to the line on the ball (I almost always have to make an adjustment here as my aim is terrible when crouching that close to the ball (step 2))
5) make a couple practice strokes focusing purely on the most aggressive stroke I can make and still "die" the ball into the hole during the putt's last 4-5 feet of roll.
6) make a stroke.
Seems to work. I have an Edel that was fitted to me without an aim line on the head, so I wasn't sure if this would screw up my eye or not. So far, it's been the opposite: It has been helpful. For now, I like it. There hasn't been much second guessing about line over the ball lately, if any. I'm not claiming to make everything, but this particular routine has been my most consistent one in a while. And even if I wrote it out in six steps, I can go through it pretty quickly.
So yea, that would stink if they took the line away. Thankfully, like the others have said, they won't.
Whether it's a legitimate advantage or not, I don't know. All I can say is that I'm not good at naturally aligning myself . Often times, a square alignment feels 5 or 6 degrees to the left. It almost feels like I'm about to pull the ball or something. But I've missed putts right enough times to know what some of my bad tendencies are. The line on the ball helps me combat that.
As I said in an earlier comment I only use the line on the ball after it's rolling. I really am not even aware of it until then. I don't see any difference at all in my ability to make the putt with or without the line on the ball.
What is annoyingly important to me is an intermediate spot, hopefully within a couple of feet of the ball. On very pristine greens sometimes it's either hard to find a spot at all or the spot can be lost after setting up to the ball. Problem is that it's a huge key to my ability to hole putts.
On days after fertilizer has been applied to the green and the specks are still visible I am almost always going to have a really great day of putting because a highly visible intermediate spot is always available. Happens way too many times, and it's way too big a difference, for it to be a coincidence.
When I'm not lazy and practice putting down the line on my oriental rug the carry-over is that the next day when I'm on the green I can actually "see" that line on my rug right there on the green. On those days I have no need for the intermediate spot and still putt very well.