My main criticism of cap and trade is twofold:

1) it doesn’t actually reduce emissions, but allows the emissions to be traded among various entities;
2) the costs of this will be passed on to the consumer - companies aren’t going to internalize the cost, but pass it along to the consumer.

If you’re a low-emitter, you can sell your share to others (which under fiscally responsible corporate boards would be the prudent and right thing to do for shareholders and those accountable for profits). That means that your share gets sent to someone else.

Governments can say that they want to reduce emissions by X in a given year, but it isn’t in their national interest to do so - they need economic growth. It runs contrary to the need to reduce emissions to meet targets.