Why has an audio amplifier negative feedback?
Typically, OpAmps on their own have a very large gain, typically tens of thousands.

So, take the setup you suggest:



In this case we are using the basic gain of the amplifier:

Vout = gain x (Vp - Vn)

So a very small voltage difference at the inputs will appear at the output multiplied by 100,000. A tiny input signal of 1mV peak to peak will come out at 100V peak to peak! Well, this is impossible and the output will simply clip at the voltage rails (the voltage will not exceed the op-amps voltage supply). This will sound horrible if this is an audio amp.

Now let's take another example:



In this case we have maximum negative feedback. What happens now? Imagine we start with the input signal at 0v, and the output at 0v too. When the input signal rises by 1mV, the OpAmp wants to increase its output to 100v. So the output starts to rise rapidly. But the output is connected to the negative input! So as soon as the output reaches 1mV, the two inputs are at the same voltage, and the OpAmp is happy. The output voltage stops rising. In this situation, the output will always match the input. This is known as a voltage follower.

Now for an actual amplifier:



In this circuit I've created a potential divider between the output and the negative input. The voltage at the negative input will always be half the voltage at the output. So now, when the positive input rises to 1mV, the OpAmp's output will need to rise to 2mV before the two inputs are at the same voltage. This set up is an amplifier with a gain of 2, because the output will always be twice the input voltage.