you know, i'm not even sure i'd want to think of an op-amp as a general purpose amplifier. sure, for very small signals with modest amplification requirements, it's true. but not generally as a power amplifier like for your stereo.
the real magic of op-amps is that they do a wonderful job of analog signal processing. and the first thing you want to get right is to not change the signal you're examining. if you load the signal with your input circuitry, you change it. op-amps overcome this by having a very high input impedance. next, they are fast and accurate, adding very little noise to the processed signal. and if you've ever taken an electronics course where you've designed multistage amplifiers using discrete transistors, you will quickly appreciate the handiness of an off-the-shelf component that does this better than you ever could do on your own.
now, once you've done some signal processing/preamplifiction with your op-amps, you may feed this into some power amplifier stage if say you want to drive speakers on a sound stage. and there you will be using discrete transistor output stages. but these will also be limited by some driving voltage, even though it's higher than +/-9V. that's just life, you will always have a limit. and that's where design comes in, managing all your constraints.
as for the question about a constant DC voltage source... lets say the load is a pair of ear buds for listening to music from you ipod. delivering a constant DC source to that load would mean that no sound waves are generated from the speakers. the signal has to be dynamic (variable AC). and the signal has to be lower than the voltage that would damage the speaker, which makes it important to have an amp that actually does saturate - it provides protection.