Basic question on Ohms law and current
...why would the LED just "draw" the 30ma it needs.


LEDs don't work that way. A 6 V. 100 mA lightbulb does, so apply 6 V to it and it will draw around 100 mA.

LEDs are different, they start to draw very high currents if you apply just a little too much voltage. If you would apply 9 V to a single LED, it would draw so much current that it immediately damages or destroys itself.

Then why not just apply the right voltage?

That won't work either because there is no "right voltage". OK, we could measure what the "right voltage" is to for example, make 30 mA flow but when the LED warms up, the voltage should change to keep the current at 30 mA. If you change the LED (even if it is the same model), you need to re-measure the "right voltage".

That's all extremely inconvenient and there is the danger that the current becomes too high due to whatever circumstances. So for LEDs we have to make sure that they cannot draw much more than for example 30 mA. That's what the resistor is for, it stabilizes the current so that the current remains roughly 30 mA even when the LED heats up, or is exchanged for a different one.


  the 9v battery doesn't have an intrinsic amp rating,


Devices that supply a constant voltage (like a battery) have a current rating. That does not mean that the device will deliver that current, it means it can deliver a current
up to that value. So a 9 V, 1 A supply (could be a battery as well), can be used up to 1 A. So 100 mA is OK, 1.2 A is not OK.

How much current is actually drawn is indeed up to the circuit, same as with the LED + series resistor.