Here is my take on the topic:
Unless you have a very radical engine, and or live in a hot part of the country, I think the answer is no. Mostly they are for the purpose of authenticity.
In fact; I have heard that if you do not need it, but have a functioning one, the
oil may stay so cool that the moisture will not burn out of the
oil, and you could have gunky, white "mayo" in your engine.
I have an
oil cooler, and I have made a clear polycarbonate cover to block the air from passing through it. My oil temperature is now at least the same as the coolant temp.
It was cooler before!
My issue with the white gunk was due to the intake manifold being installed to far back, exposing the coolant port to the oil system.
but: I still keep the oil cooler blocked off.
I hope this helps.
Don C.