Economists have studied Pigovian taxes a lot. There are answers to most of the obvious objections (and answers to those answers, and so on). I happen to think most of macroeconomics is pseudoscientific nonsense. Unfortunately, in cases like this, pseudoscientific nonsense is the best we have.
Putting tariffs on Chinese goods isn't exactly an unpopular idea either.
Insofar as the atmosphere doesn't confine itself to political boundaries, it certainly seems to me like that would be the sensible way to attempt such a thing. Why faff around?
Companies that don't want to pay this tax would, of course, be free to simply not sell their products in the USA. But I doubt that every participant in, e.g., China's consumer product manufacturing industry would be able to stomach such a course of action.
It would be similar for a hypothetical sugar tax. Which, of course, the US already has something like that, but of course it's currently being used to favor domestic sugar production over international sugar production, so it's not applied consistently to all sugar. But still, I think we can see from that that it's not a question of practicalities. If we can do it for the sake of economic protectionism, then I'm sure it would also work when the motivation is to mold people's diets.
(In case I need to put a finer point on it, I'm speaking here about the feasibility of actually implementing an excise tax policy; I'll refrain from speculating about its ability to achieve its stated goals.)
Long story short, I think that this sort of thing is probably less a question of practicalities than it is a question of political will. If you have political reasons to like this idea, it's very easy to come up with motivated reasoning for why it would be something approaching a panacea. If you have political reasons to dislike it, it's very easy to come up with motivated reasoning for why it could never work.
I'd say it's harder to create a measure of carbon output for a given finished product that is remotely accurate. It really depends where each part of the pencil was manufactured, what specific materials are used, what manufacturing processes were applied, how each raw material was shipped, etc. Take that multiply it by a billion products and you have a huge mess.
If you want a good explanation for what excise taxation's about, albeit one that uses stodgy, old-fashioned language, you need look no further than Adam Smith's writings on the subject in The Wealth of Nations.