Operating cost of renewable energies is relatively small compared to the fossil-fuel power plants. The major part of the total operating cost is due to the fuel cost. However, wind turbines have low operating cost and high capital cost. It should be noted that wind power cannot necessarily reduce the operating cost of the system. You should also consider the cost due to managing the wind power intermittency.
Idea for using renewable sources, wind power, solar, etc. is to decrease impact on environment, dependency of fossil fuels and start to use cheap energy which exist all-round the globe. Wind power have some cost but it decreased constantly with technology development. In general, wind farm operation cost decreased. It have impact on total cost operations for power system but also it is decrease constantly. Operation cost increased for Transmission system operators and Distribution system operators. In general, push operators on new level for controlling the network, they are use new technical solutions for controlling the system and develop new forecast tools. At the end operations cost of whole power system decreased.
Yes the fact that not just fuel but also variable O&M cost of wind turbines is regarded as zero is the main reason. Note though that there are some cost implications that do not easily meet the eye: (a) fixed O&M cost for wind is regarded quite high and if you believe the US Energy Information Administration's Annual Energy Outlook figure (April 2018) - it is $47470/MW/year. This is in fact a lot higher than most conventional thermal generation; (b) there are indirect costs to the system to manage the variability of wind including the cost of spinning reserve, voltage support and even back-up generation for periods when wind yield is very low (e.g., the pre-monsoon season in India in April/May when demand is actually quite high). So yes the operating costs would be lower as the cost of the technology has dropped to just 3-4 c/kWh but not as low as is often made to be for these hidden costs.