Balanced impedence?

Can anyone explain why, when running balanced connections between a preamp and power amp, the output and input impedences should be equal? With single ended connections it makes sense that a low impedence ought to mate well with a vastly higher impedence. Why are balanced connections different, impedence-wise?
They should not be equal. If the input/output impedance of a preamp to amp are equal, you have a maximum power transfer between the two. This is nice, however since each component has its own power supply, it's a useless nice. What is important is that the preamp's AC signal voltage is preserved as much as possible to the amp input. So, by increasing the amp input resistance with respect to the preamp output resistance increases the input voltage at the amp (voltage matching). The impedances are in series; so a larger Z differential means less current, less power but more voltage by simple Ohms law. The power suffers, but so what - with an infinite input Z the input voltage approaches the driving voltage. That's what an amp's input/driver stage looks for - as high a voltage signal as possible since it gains up the voltage, not the power.

This applies to balanced as well as single-ended signal transfer.
Thanks for your response Gs. I now see that many power amps do typically offer high balanced input impedances.

What led me astray are these lines from the Threshold S/350e owner's manual: "The balanced setting provides a standard 600 Ohm professional connection, and the unbalanced setting provides 50,000 Ohms load through an RCA connector." and later, "Moving the switch toward the XLR connector will select a 600 Ohm input characteristic. Moving the switch toward the RCA connector will select a 50,000 Ohm unbalanced input characteristic. Make the appropriate selection as required by the equipment sourcing your Threshold amplifier." and finally in the spec sheet, "Input impedance: 50,000 Ohms unbalanced, 600 Ohms balanced." Maybe my question should be: what is the standard 600 Ohm professional connection?
Before the advent of high fidelity , conventional wisdom held that matched impedances were the way to go when transfering audio signals. I don't know why or when, but 600 ohms developed as a standard and still holds today for some applications. I believe it has to do with the fact that earlier systems tended to be transformer coupled and input transformers tend to have lower impedances.

Noise rejection is one advantage of this lower input impedance. If noise currents are induced in the cables, they will develop lower voltages at the input because the impedance is lower. (Voltage = current x impedance)

I found this link which may help a bit.
Thanks Herman, the link is helpful. Given the link's explanation that a matched impedance connection will attenuate the signal by 6dB and thus require 6 dB more gain, can I assume, that because balanced signals typically double the output voltage, that using matched impedances is a way to gain-match balanced connections with signal ended connections, or maybe compensate for the voltage doubling rather than ignore it?

In the past, I've noticed that running a low impedance balanced source into a high impedance preamp connection raises the overall gain in the system and reduces the useful range of my volume control. I've not used the balanced input on my power amp but I'd like to one day. I'm still searching for its contemporary preamp or a suitable substitute that I can run balanced.

Electrical theory aside, I can see how a standard could be useful to an engineer who might wish to preserve favorite or sweet-spot control board settings. Thanks for your comments.