A tax is actually vastly more complicated and easier to game.
Remember, the goal is to cap emissions, not to raise money. When you start with a cap and work backwards towards the clearing price, you are guaranteed to be meet that cap. But when you start by setting a price, there is zero guarantee that you're going to meet your emissions target.
Also, the point of cap and trade is that it lets societies meet their emissions target in the least expensive way possible. Whereas a tax imposes the same fees on everyone, regardless of how much it would cost them to lower their emissions. This makes zero sense.
Remember, the goal is to cap emissions, not to raise money. When you start with a cap and work backwards towards the clearing price, you are guaranteed to be meet that cap. But when you start by setting a price, there is zero guarantee that you're going to meet your emissions target.
Also, the point of cap and trade is that it lets societies meet their emissions target in the least expensive way possible. Whereas a tax imposes the same fees on everyone, regardless of how much it would cost them to lower their emissions. This makes zero sense.