The Wikipedia equation there mentions the formula ignores the contribution of the internal resistance, which would make it proportional. It seems the article assumes that resistance is a significant contribution (possibly even just from their voltage source) while you assume it is not, for any given particular diode being evaluated or measured, either could be right

Wikipedia says:

> Internal resistance causes "leveling off" of a real diode's I–V curve at high forward bias. The Shockley equation doesn't model this, but adding a resistance in series will.

For small diodes and all LEDs as far as I know, it will level alright. Leaving behind a cute little smoldering crater where the now vaporized diode used to be.

https://www.onsemi.com/download/data-sheet/pdf/1n4001-d.pdf

Take this very generic diode here. When mounted as instructed for the highest heat dissipation, it should gain 50°C per Watt. The flattening of the Current-Voltage curves starts at around 1A. As the diode heats up, the resistance lowers. Extending the limits.

Maximum before damage is 150°C. Minus 25°C ambient leaves us 125°C. Divided by 50°C/W gives us 2.5W. Around 2.8A-3A at 0.8V-0.9V forward voltage.

But the curve is barely proportional at 5A. You might also notice that the datasheet doesn't provide numbers beyond that point. Presumably because the diode left the room then.

In practical diodes it's much more likely to be a minimal contribution.