Most of them actually cause damage to the engines by preventing the engine oil from getting to full operating temperature .
Small engines are fitted with coolers if they are going to be used in equipment that operates for very long times continiously like in skid steers , generators & compressors
Unless you are a commercial mower and mow 25 acres in a single session then again the oil coolers are potentially doing more harm than good unless you fit a very expensive one with a thermal bypass valve .
In general I agree with your statement -
Oil Temperature
I was trained to encourage crankcase oil to reach at least 100 C at least once in an operating day. This is to drive off volatile contaminates such as water, fuel & byproducts of combustion, all of which can reduce the efficacy of the oil and thus cause engine damage.
Most engine oils are quite happy to continually operated in the 100 -120C range, although probably better at the 90-100C range
Thermal Bypass/Thermostat
A thermal bypass/ thermostat only works to speed the temperature rise of the oil OR in very cold climates maintain it above a preset level.
Oil Coolers
An oil cooler is just a devise (there are several types) that supplements existing oil cooling capacity.
One should only be fitted when there is a known deficiency in the standard cooling system.
As you point out, overcooling can certainly have a negative effect on the life of the engine & fuel consumption.
If you are considering fitting an oil cooler, I strongly suggest you start by fitting an oil temperature gauge - Monitor the temperatures reached during operation - If you start to see temperatures getting to about 130C then an oil cooler may be indicated - I say may be, because a good clean of the engine cooling system may deliver lower oil temperatures, without the added expense /complexity of an oil cooler.
