You will find that US-based carriers will be quite consistent, as the rules for the use of these items are mandated by US federal law. (Specifically the Code of Federal Regulations, 14CFR121.311.) Both the US and Canada ban the use of seatbelt extensions (aka "belly belts") on the grounds that if there is sudden decelleration of the aircraft, the child is apt to become a human airbag.

As far as I have been able to determine, EU governments seem to leave these policies up the the airlines' discretion.