But the stock intake usually strangles the induction pathway so much that anything is an improvement, as long as you don't go too large and lose that mid-range.
A larger oil filter helps in that it allows you to run more oil. More oil means more protection from lateral-G induced oil starvation, and more fluid medium to absorb heat. That's at least half of the benefit of an oil cooler. An oil cooler set-up has more oil to resist starvation, more fluid medium to absorb heat, and a heat exchanger to remove that heat from the fluid.
I wonder if my engine would have survived without the cooler? I did one road trip of just over an hour spending about half that time close to redline, with some stretches where the car is pegged to redline. (disclaimer: I don't live in the United States). When we got to our destination, in the middle of absolutely nowhere... I was over 1 liter down... but thanks to the oil cooler, my capacity is about 5-6 liters, so the engine was still well oiled and I got home with no problems.