As you may be aware, the US is a confederation of states. The type of light that flashes several times at the initiation of braking is specifically authorized by the California Vehicle Code, and perhaps in other states.
Do you have a reference as to where it's allowed in the CVC? FMVSS section 108 table I-c specifies this for the stop light:
Steady burning.
Must be activated upon application of the service brakes.
When optically combined with a turn signal lamp, the circuit must be such that the stop signal cannot be activated if the turn signal lamp is flashing. May also be activated by a device designed to retard the motion of the vehicle.
(a) Any motor vehicle may also be equipped with a system in which an amber light is center mounted on the rear of a vehicle to communicate a component of deceleration of the vehicle, and which light pulses in a controlled fashion at a rate which varies exponentially with a component of deceleration.
(b) Any motor vehicle may be equipped with two amber lamps on the rear of the vehicle which operate simultaneously with not more than four flashes within four seconds after the accelerator pedal is in the deceleration position and which are not lighted at any other time. The lamps shall be mounted at the same height, with one lamp located on each side of the vertical centerline of the vehicle, not higher than the bottom of the rear window, or if the vehicle has no rear window, not higher than 60 inches. The light output from each of the lamps shall not exceed 200 candlepower at any angle horizontal or above. The amber lamps may be used either separately or in combination with another lamp.
(c) Any stoplamp or supplemental stoplamp required or permitted by Section 24603 may be equipped so as to flash not more than four times within the first four seconds after actuation by application of the brakes.
Steady burning. Must be activated upon application of the service brakes. When optically combined with a turn signal lamp, the circuit must be such that the stop signal cannot be activated if the turn signal lamp is flashing. May also be activated by a device designed to retard the motion of the vehicle.