Later this summer, the USGA and the Royal & Ancient will address whether the position of the hands and arms when using a belly putter constitutes a new, separate way to putt a ball, and thus not legal in tournament play. These organizations struck down a croquet type stroke and billiard cue stroke, and are concerned about the way belly putters are anchored to the torso, as anchoring is distinct to these putters. The R&A seeks to limit the range of movements a player can make while using a golf club.
Unconventional grips, set-ups or swings are usually called into question if they show up on the Tour. The belly putter includes all three in some ways. I would not be surprised if putters longer than 40 inches were disallowed in 2013.
Belly putters are a great tool for practicing, especially if there is a tendency to get wristy or to move one’s hands in the putting stroke. However, these putters look like a crutch, and when two majors get won by players using them it can look like cheating.