Why does the voltage drop across an LED matter when determining an appropriate resistor value?
In short, it matters, because the LED needs some voltage over it to work, so some part of the supply voltage will be over the LED and the rest of the supply voltage is over the LED. Only the resistor obeys Ohm's law and the LED doesn't. So only the voltage that is over the resistor and the resistance determines the current that is passing through the components. You can test this yourself by measuring voltages. Make a LED circuit and use 5V supply and known resistance such as 1kohm. If there is 2V over the LED, it means there must be 5V-2V = 3V over the resistor. If you want to calculate current, you must choose if you use supply voltage 5V to get wrong result of 5mA, or voltage over the resistor to get correct result of 3mA.
You can of course have a rough estimation for the resistor value by ignoring voltage over LED and just use supply voltage.
But the estimated resistor value would not be accurate and actual current will be less than desired, because the resistor will not have the full supply voltage over it like in the estimation.