Yes, but maybe steel is more essential to society than burning natural gas. But natural gas companies make more margin so they can afford the carbon credits, meanwhile steel has tighter margins so it gets passed to the consumer. This means it might disproportionately limit the consumption of things based on how much money they make. This is all fine until construction becomes more expensive because you can’t easily get the steel you need for buildings (what if you were trying to build a clean energy power plant and. Is it’s too expensive?). Some things are essential and need protection from the free market (ex, hospitals have diesel backup generators. Those would become more expensive). You could add a government subsidy for steel, but now you’re stacking laws on top of each other and playing centrally organized government. Which doesn’t work well.
The downside to having separate laws per industry is that you’ll get insane workarounds (see import tariff law). Carbon is carbon — so workarounds are easy. For example if natural gas is taxed higher than steel, you’ll have natural gas companies producing just enough steel to be qualified as steel production companies so that they get the lower rate. Or something like that.
Choosing policy is tremendously difficult. We could deliberate all day. despite what I’ve said, a carbon tax is better than doing nothing, and we would be wise to start creating/increasing carbon taxes already.