Input impedance of High - Frequency Amplifiers
In the RF domain you already mention that what is important: impedance matching.

Fact is that RF signals generally have such a high frequency that the wavelength of the signal can come close to the length of the tracks on a PCB and/or wires between PCBs and connectors. That then means that we cannot use "just a wire" the wire needs to be a transmission line.

Note that a transmission line can be made using a Coaxial cable but also can be made by drawing a "controlled impedance" line on a PCB. Look on a PC motherboard PCB, the lines to the memory slots and high speed lines like SATA and USB connections are all controlled impedance lines.

For a transmission line to work properly (transport the signal from A to B while not distorting it) the begin and end of the transmission line need to be terminated properly. This means that the input and output impedance of the circuits to which the transmission line connects must match impedance wise. The most commonly used impedance for RF transmission lines is 50 ohms.

When a transmission line isn't properly terminated signal reflections will occur and these distort the signal.

For low frequency signals these reflections aren't a real issue so we don't need the impedance matching and can choose the impedance that is most convenient.