While researching the standard method of measuring fall time (and rise time) it seems to be standard to take the start and end points for measurement to be when the curve is at 90% of the maximum and 10%. However, I'm having trouble pinpointing an exact reason as to why this is. Any help would be appreciated!
10% to 90% has evolved as a de facto standard. It could easily have been 20%-80%, or 5%-95%. But it wasn't.
When you make a measurement, you want it to be reproducible, which means going through the trigger point with a reasonable slope.
When you make a common measurement, you want it to cover as many cases as possible.
Using nice round numbers like 10% and 90% has satisfied enough people on these two points that they keep using it, even though it might not be exactly right for the specific system they're using.
The reason is that the rise/fall voltage curves are actually exponential RC charging curves. The output resistance of the chip charges the capacitance of the wires and inputs connected to it, forming an RC lowpass. The output voltage of the chip might in fact never reach 100% of the supply voltage, especially if there's a DC load on the output which causes additional voltage drop across the output's internal resistance.
10%/90% is chosen because pretty much any logic input will recognize these levels correctly as low/high. TTL, for example, runs at 5V and recognizes anything below 0.8V as "low". 10% of 5V is 0.5V, so after the specified fall time of the logic output, any connected TTL input is guaranteed to recognize the voltage level as "low". It doesn't matter how long it takes to reach the full output voltage level as long as the logic threshold is passed quickly.