I was the first to win a major with a belly putter, and I've spent hours practicing that way, so I hope they don't ban anchoring.
When I throw a softball, there's no time to think about the motion of my arm. I just look at the first baseman's glove and react.
The beauty is, while you're working on chipping, you're also working on driving. This is because the bottoms of both swings - the area around impact - are identical.
It's such an advantage to be able to hit short irons low on command. When it's windy, you'll hit more greens. But low shots are a great strategy in calm conditions, too: The less time the ball hangs in the air, the less time it has to stray off line from the flagstick.