Why is input impedance matching done for amplifiers?
Impedance bridging is done if you are interested in Voltage rather than Power. It will ensure that maximum voltage is driven to the amplifier input with minimum signal degradation. It consumes less input power, as the current drawn by the series combination of source and load impedances is low. It is relevant in voltage amplifiers.

Impedance matching is done when you are interested in Power. It is relevant in Power amplifiers, where output loads are of low resistances. Here the input impedance is equal to the source impedance. The amplifer will now extract maximum Power off the source at its input (MPT-Theorem). Compared to previous case, the input current of the amplifier is higher too. Hence, the amplifier can now drive higher current in the output collector circuit. i.e., More Power can be extracted at the output. Also, it is not just about the output Power. It is also about Power efficiency in terms of input power and output power of the amplifier. Maximum Power efficiency is obtained only when the impedances are matched.