I don't think I'd ever put an oil cooler on my Jeep. The block temperature is regulated by the cooling system, the thermostat, fan and radiator. If you run cool oil through the block the coolant will rise in temperature to maintain the correct block temperature. If you run hot oil through the block the coolant will run cooler to decrease the temperature of the block. As the engine is running the oil and coolant both play roles in cooling the engine but you don't need two systems to regulate the temperature unless one of them can't keep up. Since the cooling and oil passages are closely coupled in the block I don't see any need in our case for another cooler. The end result of a very high performance oil cooler is slower coolant flow which doesn't seem like something I'd want.
As long as you're running a thermostatic oil cooler of a reasonable size, that feedback echo tends to be a non-issue.
The linked cooler is only rated to about 21,000 btu/hr of maximum heat rejection. (You can buy bigger ones of course.) Plus the thermostat ensures that oil that is too cold does not continue to get overcooled.
Meanwhile, driving at 70 mph on an average freeway, I get about 13 MPG, equivalent to 5.4 gallons an hour. A gallon of gasoline has about 116,090 btu. So you are burning 627,000 btu/hr. Roughly 30% of that is turned into power, or 73 horsepower. (Some of that is then lost in the drivetrain, engine friction, and belt drive.) Another 40% leaves the tailpipe. The remaining 30% leaves the cooling system. That's 188,000 btu/hr leaving the radiator.
Thus the addition of an oil cooler doesn't negatively impact the ability of the cooling system to cool. It can just as easily reject 165,000 btu/hr as 188,000. The thermostat just doesn't open quite as far. The rest of the coolant gets pumped through the heater core and remixed with the cooled coolant before recirculating through the block.
As to in the block, the advantage comes that the oil and coolant are now at more consistent temperatures. More consistent engine temperatures result in lower thermal stresses, and less overall wear.
In addition, since the oil temperature is thermostatically regulated, it now has a more consistent viscosity across a wide range of operating conditions. Thus less dramatic swings in oil temperature and viscosity occur, reducing the odds of engine wear from excessively low viscosity at high temperatures. The thermostat protects against high viscosity caused by overcooling.
Thirdly, reducing the peak temperatures of the oil will extend the life of the oil, allowing it to keep its properties consistent for a longer period of time. Theoretically you could extend your oil life interval, but I wouldn't recommend this for other reasons.
The only two scenarios I could see causing an issue would be a massively oversized oil cooler, or a non-thermostatically controlled oil cooler. If the oil is not hot enough, it will not lubricate as intended and it will collect moisture and fuel vapors.