It all depends on type and what the manufacturer and operator have specified in the "books".
On a 737CL/NG there is absolutely no need for this "invented" check, I would not even know why there would be a limitation. It is absolutely true there is some "airmanship" that goes beyond procedures, but that airmanship in this case to me only relates to the gear "initiation", meaning: the indication of a correct release of the gear. The gear down sequence takes way too long time to complete and having pilots focus on the gear indicators while flying just seems waste of time. It is much more "safe" to create a gentle idle slowing down while the flaps are extending focusing on correct pitch changes and glide tracking, than asking pilots to increase thrust all of a sudden because one apparently needs to see 3 greens and creating only extra workload. Keep it simple.
For what it's worth, if it was simply a B737, there is a lot more to say about decelerating to correct speeds when asking for flaps to be extended than waiting for 3 greens... And that is a Boeing demand mentioned in the FCTM. The 3 greens requirement is not a Boeing demand.