Analysis: "The vast majority of legal precedents say clearly and unequivocally that governing bodies like the USGA enjoy unfettered authority to determine the rules..."
If the golfing authorities were attempting to ban the long putter itself, there may be some relief in the courts for equipment manufacturers, but even that would not be not a sure thing. The change being considered, however, is not a ban on long putters; it's a change in the definition of the golf stroke that would prohibit anchoring the long putter against the chest or the body.
In some circumstances, litigation or the threat of litigation can become leverage in a settlement discussion with the ruling body of a sport. The square-grooves-on-golf-clubs controversy is one example. But the legal basis for any claim on anchoring is so weak that the litigation would end before the players could begin to negotiate for, say, a grandfather clause that would allow them to continue to use their long putters but ban anchoring for new players.