Once government subsidies are removed, can wind power, on average, compete on a large scale with traditional power sources?
Assuming a market rate of $.10/KWh, and the wind farm is located on the prairies in an area with plenty of wind, what kind of profits would there be?

Wind power is profitable, although it takes a while to be.
And… how far is that prarie away from a city?
Eventually, the wind turbines would pay for themselves. However, they are very expensive, about $70,000 to power a home. Then, they need repairs every three to five years. However, eventually it will pay for itself, and it is good to be independant when it comes to energy.
Assuming you paid them $0.10 for their power, then yes they would be. But the wholesale rate for electricity is generally lower; maybe half that.
For example, the Roscoe wind farm cost about $1.25m/MW of capacity. Assuming wind resources are UK average, the capacity factor will be bout 30% (UK average is 28-31% depending on year). Therefore each MW will generate about 2.62 million kWh/year, or $262k/yr.
The Danish Wind Energy Association claims that maintenance costs are under 3% of initial outlay, so you should expect that over a 25 year life, excluding decommissioning costs and assuming $0.10/kWh, a wind turbine has a yield of about 8% annual return, assuming that you put aside the maintenance money at the beginning, an annual rate of interest of 3% and a rate of electricity inflation of 3%.
Assuming $0.05/kWh, then the rate of return is just under 5% over the 25yrs.
In general, coal is cheaper than wind without subsidy; but we can’t really tell how much. In the US, the subsidy is equivalent to about 1.2 cents/kWh, and that has led to an explosion of wind power. Since I’m not aware of any countries that have large wind power without some kind of encouragement, I can’t think of any empirical data to show just how competitive wind is.
That said, there are very good reasons for either taxing coal or subsidising wind. Coal adds social costs in terms of billions of dollars in healthcare and agricultural damage from air pollution plus the social costs of climate change. Considering these costs are typically estimated at between 1-10 cents per kWh, the US subsidy looks justified to me.