Whyso? Light travels at c in all reference frames. All we would see is those signals changing in wavelength.
Please read chapter on black holes from Sean Carroll`s book or free online notes on General relativity.
This is true that signals would be redshifted. But also they would reach us with interval between two signals increasing as object approaches event horizon.
You are right that light travels with speed c. But distance between two points with coordinate separation (dr) is not just (dr).
But rather it is determined by metric as well.
Scwarzschild metric has (12GM/r) factor in denominator accompanying (dr)**2 .
Hence distance between two points with same coordinate separation would increase if we are close to event horizon.
Hence separation between the signal sent by person sitting on object falling into blackhole would increase as object approaches event horizon.
Because distance between two points is rendered infinite by the metric.
