By my real world experience, income taxes make me charge more than I would without it. Is that in opposition to your position?
The Theory of Perfect Competition is based upon the assumption that no single participant in the market can affect the market price. Now changing that assumption requires that the theory change to accommodate the new situation.
A small business in a market which does not have all the assumptions in place required by the ToPC does not follow the Model. Therefore you do have more control over the price you charge but it is limited as you know since you cannot charge ANY price you wish. But that cannot be extended to sectors which have more of the assumptions in place. In addition, we must distinguish between the short run impacts and the long run. Say you have the only gas station in town and decide you want to charge the monopoly price of $5 a gallon. You could get away with it for the short run but in the Long Run someone is going to realize that you are making a higher than normal rate of profit and open up another station.
Theory is a means of getting a grasp on how an economy works I try not to make it a straightjacket beyond which one cannot move. Knowing how to adjust the model as the assumptions are violated or removed is crucial.