Yes. But then input and output impedance should depend on the closed loop gain and not bias scheme. Here R1 and R2 are being used to bias the transistor such that it operates over the linear part of its curve. If we use less than 10x the base current then that will only increase device dependency. 10x gives a very good margin in that we don't have to hand-select devices.
This is not that much of a concern for switching applications, where all we care about it turning the device on/off - of course some rules apply hear as well. But for linear (analogue) applications this takes on more significance...