I am pretty sure that an "infant belt" is illegal for U.S airlines (I assume that this would be the same as a belly belt?) -
F. CRS Performance in Passenger Seats. In 1994, the FAA issued a study entitled “The Performance of Child Restraint Devices in Transport Airplane Seats.” The research for the study, conducted by the FAA Civil Aerospace Medical Institute (CAMI), involved dynamic impact tests with a variety of CRSs installed in transport category aircraft passenger seats.
The FAA used the results of this study as the basis for prohibiting the use of the following devices during ground movement, takeoff, and landing. The CAMI study revealed the following observations:
1) Belly Belts. These devices attach the child to the accompanying adult. An abdominal belt attached to the adult’s seatbelt restrains the child. During dynamic testing, the forward flailing of the adult and the child resulted in severe body impacts against the forward seat. The child Anthropomorphic Test Dummy (ATD) moved forward to impact the forward row seat back, followed by the adult ATD torso striking the child ATD. Then, the adult ATD torso continued to move forward after contact with the child ATD, crushing the child ATD against the seat back.
2) Harness Restraints. The devices that CAMI tested consisted of a torso harness for the child ATD placed in its own seat with the airplane seatbelt routed through a loop of webbing attached to the back of the harness. During dynamic testing, the devices allowed excessive forward body excursion, resulting in the test dummy sliding off the front of the seat with a high likelihood of the child’s entire body impacting the back of the seat directly in front of him or her. Then, elasticity in the webbing of the harness and seatbelts pulled the ATD rearward and this rebound acceleration presented further risk of injury.