Cap & trade is an attempt to remove the preferential treatment presently given to the fossil fuel industry. That has been well documented, and exhaustively studied.
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Really? What studies? The only actual "subsidies" are externalities and that's hard to calculate. The government does not give money to the oil and gas industry. Actually we have become more efficient in our use of oil and gas. Today each 1% growth in GDP requires much less use of fossil fuels than in the past. 
If you are looking for government subsidies look no farther then the wind and solar industries. The wind and solar renewables still require gas pants to back them up.  Even electric cars require subsidies. When governments stopped the subsidies car sales plummeted.