electricity - Why do Generators generate inconsistent voltage?

I'm ultimately trying to understand the function of resistors in a circuit. The way I see it, a small increase in voltage could result in a high increase in current that would "burn out" an LED if there is no resistor to ensure that the correct amount of current reaches the LED. So what causes a Generator to generate inconsistent voltage that would call for a resistor in the first place?

Answer

It's not merely “a small increase:” any voltage operating over zero resistance drives an infinite current.

Nature abhors an inifinity, so in practice you drive things out of their predictable regimes. Without the resistors there you may start to notice all of the ways that your other components fail to be ideal, like your power supply’s input impedance or the resistivity in your wires. These are hard to predict and hard to control over time. Other components like inductors and capacitors can also absorb the infinities, but they have their own complications—in particular, LC-circuits are prototypical oscillators and you might have trouble building systems in a quiet, predictable state.

In fact, resistors cannot smooth out irregularities in power supply voltage: they transfer it directly to irregularities in current. If you want to smooth that out in a DC scenario, you want a “low pass filter:” you either want a capacitor in parallel with your load, so that dips in the power supply’s voltage are temporarily supplemented with the capacitor’s voltage while peaks are greedily absorbed by the capacitor first, or an inductor in series with the load, which does the same vis-a-vis the current. If you want to target a specific cutoff frequency for such a filter, resistors also become indispensable for that.

We need resistors as voltage dividers and to take a fixed voltage difference and convert it to a predictable low current independent of the details of the wiring and the power supply. We need them to damp out oscillators that we create with inductors and capacitors. But we don't use them to make our power supplies more uniform, because they cannot store energy, they can only dissipate it.