If I'm not mistaken, between PONY, Little League, and ASA, ASA is the only one with this rule. In PONY and Little League, batter-runner is entitled to first base, but may advance beyond at their own risk (provided they follow the "look-back" rule).

Somebody can correct me if I'm wrong, but in ASA 10-U, the ball is not immediately dead. Rule 8-H-4 says, "...If the batter-runner advances further, once the ball becomes dead, return the batter-runner to first base." Which means, according to Rule 8-H-1, "A runner, attempting to advance beyond the one base they are entitled to advance or steal, may be put out while between bases."

Hope this helps.