You tax carbon, country B now has an advantage over you.
You loose!
Now all your products are produced in country B, you've changed nothing and country B is probably using coal so you're worse off from your initial goal.
Why do people think "enforcement is impossible" is such a strong argument against taxes?
If your argument is that tariffs don't disincentivize behaviors because the government is just that bad at collecting taxes, you're not really in step with reality.
But you can't enforce your taxes in other governments.
In fact other governments in a game theory like ploy to get ahead of your country may agree to international agreements that they know they can game to their advantage.
The fundamental assumptions are wrong. You're not in this together. All countries are in direct competition, and some a more cut-throat than others. If potential disaster B is coming irregardless, country B can position themselves to come-out on top of country A when it does.
An argument could be made if we don't apply the Carbon Tax to poor or third-world countries it will help them develop faster... but those third-world countries shouldn't be shipping us resources in the first place!
Name one international treaty that has ever had teeth where the benefits of non-conformance out weight the teeth.
Country B could tarrif country A in return and some countries cannot afford the cost of what that may do to them.
So you end up with an international treaty without international conformance or a treaty with no real teeth because the signee's have contributed to it what would allow "them" to game the treaty.
And funnily enough, it's still lower than it would have been without the treaty. It's almost as if compliance doesn't have to be perfect to be effective, fancy that.
Nations agreed on laws for ocean and air travel. Countries that disobey them are ostracized or even subject to violence. Nations could in theory do the same for polluting the ocean and air. But that gets viewed as denying developing countries the benefits developed countries had.
If it worked it wouldn't be happening, the fact that it is happening, and to well known country's proofs they don't work and is profitable for country B and C for it to continue to not work.
This not withstanding the obfuscation of country of origin that can happen If country B and C really wanted to work together.
Now all your products are produced in country B, you've changed nothing and country B is probably using coal so you're worse off from your initial goal.
You loose double!