Carbon taxes are a market based solution and pretty much everyone agrees.
Unregulated pollution is basically like having unregulated crimes. Criminals obviously want to keep committing crimes because they benefit personally.
Imagine if you could just go and mug a random CEO and get $10k out of that and the police won't stop you. The CEO and even those who hate the CEO would agree that muggings are bad. The only one who disagrees is the criminal. Therefore regulation is actually necessary to have a well functioning free market in the first place. Heck, punishing net negative behavior is compatible with the free market. The only question is how that punishment is implemented.
Without CO2 taxes you basically have people legally dump waste into the atmosphere which is shared by everyone equally. It's pretty obvious that there is nothing free about this. You can consider the act of pollution to be a forced transaction between the polluter and every other living being on earth. It's like you are mugging a tiny fraction of a cent off of millions of people.
The obvious idea is to just do the same thing we did with garbage disposal. Just charge a fee that covers the damage. That way the polluter has to weigh the damage he does. In some cases the damage outweighs the benefits, in other cases the benefits outweigh the damage. As a society we only want the latter.
The only real problem with CO2 taxes is that every nation has to agree on them. That's what the paris agreement is for. Dismissing CO2 taxes entirely because of global competition doesn't make sense. Global competition merely puts an upper bound on how high domestic CO2 taxes can be without introducing special tariffs or other means of global enforcement.
I prefer a token amount over complete denial because at that point you can just point out that the price is too low instead of pointlessly arguing about which policy to implement or whether to implement a policy at all.