As I see experiments have demonstrated results that falsify this statement.As indeed no physical effect can propagate faster than light,
No. Your statement is sloppy. Entanglement is joined statistical property of two particle state. To speak about speed or propagation we have to speak about individual particles in entangled pairs. It does not make sense to say that two particle property propagates from one particle to the other one.I assume you attribute speed and propagation to entanglement.
The whole point of Bell inequality violation is to demonstrate that this can not be the case.Entanglement is a well define process that occurred at one single event. The firther detection space/time separations events are irrelevant.