Would drawing too much current cause some kind of 'magnetic damping' in the voice coil, thus preventing perfect sound capture?
Drawing any amount of current causes electrical damping to the voice coil and attached diaphragm. This is in addition to any mechanical or acoustic damping built in to the microphone design.
Note that this isn't a bad thing. A controlled amount of damping is useful to prevent the voice coil/diaphragm assembly overshooting and to control the mechanical resonances it will have. The microphone data sheet will tell you what range of load impedances you should use in order to get the best performance from your microphone. The microphone manufacturer is deliberately using the input impedance of the next stage as part of the damping design of their microphone. No data sheet? Choose another microphone if you care about the sound quality.
Changing the impedance of the following stage, typically a microphone pre-amp, may let you adjust the frequency response of the microphone. I'm afraid my ears are insufficiently golden for this sort of trick and using the EQ on a mixer is a more direct method to achieve this. (EQ = equalisation = tone controls, but don't let a sound engineer catch you using such a straightforward term.)
please correct me if I'm deeply misunderstanding some fundamental concepts here.
No, your reasoning seems to be correct. The underlying concept here is conservation of energy. The electrical energy sent out to the AC power wiring from the alternator or down the microphone cable has to come from somewhere.
In the case of an alternator the energy comes from the mechanical energy supplied by the prime mover (whatever is turning the input shaft of the alternator - a hand in your video but more usually a motor or turbine). The countertorque caused by the alternator output current provides the mechanical load that the prime mover is working against. The product of the countertorque and the angular speed of the alternator gives you the total electrical power being generated. (Directly equal if you're using SI units - watts, newton.metres, radians/second - otherwise you may also need a conversion factor). The total electrical power equals the load (the light bulb in your linked video) and also the resistive losses in the alternator armature and connecting wires.
Increasing the load (e.g. a more powerful lightbulb) will increase the current demand, in turn increasing the countertorque and hence demanding more mechanical power from the prime mover. A practical alternator system will have some form of automatic regulation of the prime mover power in order to maintain a constant speed and hence frequency output as the load varies (at least for older, pre-inverter designs).
A microphone takes its output electrical energy from the acoustic energy in the incoming sound wave. The output current flowing in the coil generates an acoustic impedance in the diaphragm that absorbs the incident sound energy and provides the energy for the electrical signal output.
why, instead of impedance-matching the pre-amplifer for maximum power transfer, [do] we use impedance bridging?
A tricky thing, the maximum power transfer theorem. It's straightforward enough to derive given some calculus (as shown in the link). It's more awkward to know when to use it, which turns out to be not that often.
It's useful when you need to recover every scrap of available power, e.g. if receiving very weak radio signals. However that's not the case with typical audio signals which are rather stronger. We have electronic amplifiers for audio which can readily boost power so we don't need to extract every bit of power from the mic. Audio circuits are usually voltage driven so it's more convenient to use a impedance-bridged connection to (nearly) double the voltage available from a microphone, compared to an impedance-matched connection.
It's also awkward to exactly define the source impedance of a microphone. It will vary with frequency, e.g. due to its self-inductance, as mentioned by Andy aka, and the effect of mechanical resonances. So it will be difficult to design a mic pre-amp that will provide an accurate complex conjugate impedance match across the whole frequency range of a mic. Then you'll have to change the matching to use a different microphone. It's much easier to provide a single, predominately resistive, input impedance for a mic pre-amp that can be used with any microphone.
As danmcb noted, a microphone might have an actual source impedance of under 200 Ω and be used with pre-amps of 2 kΩ or more. (Some Yahama mixers I use have 10 kΩ input impedance.) In the audio world this is referred to as a nominal 600 Ω line. Very nominal. This is a historical hangover from the time when line meant a telephone line and they actually were 600 Ω - a very long time ago, but not now. (When I started work in the early 1980s I worked with systems that sent (lo-fi) audio down telephone lines, presented as 600 Ω balanced connections. They were legacy systems even then.)
600 Ω telephone circuits (Telegraph circuits actually, but telephone circuits will look the same.)
Source: Wikipedia
