First, keep in mind two fundamental relationships:
Ohm's Law: Voltage = Current x Resistance
Power = Current x Voltage, which, by subsitution of the above relationship, equals ((Voltage squared)/Resistance)
(Both relationships applying to situations where the effects of inductance and capacitance are negligible).
Higher input impedance makes it harder to transfer POWER into a given load device, in the sense that more voltage is required to drive a given amount of current into that load device.
However, we are not interested in delivering power into the amplifier. We are interested in having the amplifier do the following:
1)Sense how much voltage is present at its input.
2)Provide an output voltage equal to the voltage that is present at its input times some gain factor.
3)Be able to supply enough output current to maintain that output voltage in the presence of a very heavy load, meaning a speaker whose low impedance will draw very heavy currents at typical output voltages. Thereby resulting in high power levels being delivered to the speaker.
A theoretically ideal line-level interface, such as between preamp and power amp, will be driven by a component having zero output impedance, and will be loaded by a component having infinite input impedance. The infinite input impedance will result in no current being drawn, while the input voltage will be sensed and amplified as described above.
If we hypothetically think of the preamp as developing an output voltage "ahead" of a resistance equal to its output impedance, then the fraction of that voltage which will appear across the input of the amplifier will decline as preamp output impedance rises and/or power amp input impedance falls. That is in itself of no significance as long as the values remain within reasonable limits -- the only difference it will make is that a small adjustment in volume control setting will be required.
However, the reason for wanting input impedance to be 10 or 20 times or more greater than output impedance is that neither impedance is likely to be perfectly constant as a function of frequency (particularly the preamp's output impedance, and particularly if it has a coupling capacitor at its output). If the variations of preamp output impedance as a function of frequency are not negligibly small with respect to power amp input impedance, the frequency response of the interface will be significantly non-flat.
Hope that helps.