Well, under the cap and trade system, industry lowered its costs by lowering carbon output. Under a straight carbon tax, they still did the heavy lifgting, in order to get a lower tax rate and a lower more attractive price. Classic Picovian economics, and consumers had a price incentive to pick low carbon-cost products.
Thanks to Dougie and others like him, we have this less effective and more complex version: If you pay the tax and the rebate balances and zeroes it out, then no one's any further ahead. But if you go looking for products and energy sources with lower carbon costs you'll have paid less carbon tax but will still get the same rebate. And industry will still work to lower the carbon-tax that shows as a cost on its books.
When and if Dougie proposes a carbon tax (or similar carbon-pricing plan) that's more direct and obvious as a behaviour-changer even he, with all his nasty faults, would get my vote.