I read the whole thread and I'm chiming in as a Physicist like BillO.
I, too, had a gut instinct that for my application with MOSFETs there was absolutely no need for the gate resistor.
In my view, the research conducted here has shown where the lines are. But this can be extended just for the thinking.
In physics, we define what current actually is - a rate of flow of charge in Couloumbs per unit time in seconds. This is where our contentions lie, and the first derivative with respect to time i.e. dI/dt.
Now I believe the datasheet current limits are for steady state constant current i.e. DC over a resistive load.
There is something that was briefly mentioned in this discussion but not considered further. The size of the interconnect leading to the pin from within the die is the limiting factor. It is a resistor. The die has been delidded and scanned and we can measure the actual width and read up on the depth and measure the length of the wire.
Without going to too much trouble I assumed the width at 0.3 microns due to the 130nm chip process, the depth at 0.48 microns from this article's aspect ratio of 1.6:
https://web.stanford.edu/class/ee311/NOTES/Interconnect%20Scaling.pdf. I assume an interconnect internally to be 0.5mm long at most. Someone with the inclination can be more precise.
Inputting these values into a calculator at:
https://www.allaboutcircuits.com/tools/trace-resistance-calculator/ results in a resistance of 64.8 Ohms within the Atmega 328p chip itself (at room temperature. I got the 0.3 micron number from here:
https://en.wikichip.org/wiki/130_nm_lithography_process#130_nm_MicroprocessorsInterconnects are often copper but sometimes gold.
We will be in the right ballpark. Now we add the resistance from the chip leg to the arduino pin. But we're already into too many assumptions. I just want a ballpark number and 5 Volts divided by 64.8 Ohms equals 77 mA. This is pretty close to the 88mA that has been seen experimentally.
I leave it to others to be more precise than this. My MOSFET gates will charge in about 20us so my duty cycle will be low. My average current at the frequency I use will be about 34mA which is in spec according to the data sheet and your collective experiments.
Now what gives rise to an amperage limit within the Arduino? HEAT! This is why when people want to overclock processors they cool them with liquid nitrogen. Increasing the clock rate means more electron flow which means more current, which means more heat.
I think the interconnects are a limiting resistance and would allow a steady state of 88mA if the temperature were kept reasonable. It could handle more under active cooling or submerged.
But at least we have an estimate of where this resistance and hence current limit comes from. I played with the values and substituted gold for copper. It's a bit of a wild goose chase. Obviously - if lightning hit the chip for an attosecond it would fry but the average current over a whole second would not be much. The greater hysteresis from rapid heating and cooling would reduce the life of the chip, but not too greatly - just test the temperature rise and build in cooling. Stress test it after that.
We can understand why a chip manufacturer would want to be conservative with their current ratings. But if you are a product designer, and you want to make a million units of something it is worth your time to get scientific proof on the actual limits in your use case.