When China bids to manufacture something for the world market, a variety of things go into the price they can bid: labor, shipping, materials, and pollution, chiefly (there is also research, facilities maintenance, etc). The main factors which give them an advantage are labor and pollution. Their labor advantage is internal but their pollution advantage -- the portion dumped into water or air -- they get by extracting value from a shared account. In countries with stricter pollution laws companies can't rob their neighbors to win a bid.

That being said, tariffs and other mechanisms meant to force the pollution cost back onto producers really end up being paid largely by consumers anyway. You can't tax citizens of another country. So the tariff taxes citizens of your own country. The cost gets back to the producer country indirectly in that they sell less stuff, but every time the tax is paid it is paid inside the country imposing the tariff by citizens of that country. So it works more or less according to your suggested mechanism.

The end result should be largely the same regardless of whether the externality compensation takes the form of an import tariff or user-facing retail tax. Either way customer prices rise and manufacturer/importer/seller margins drop. Tariffs are a blunt tool, but so are most consumer-end taxes as well. But coming up with the sort of Pigovian precision instrument, that attempts to fairly reflect the actual lifecycle externalities of a good or a service, is probably going to be almost impossible for several reasons.

Then you would be charging people who have no control over the production. The producer nation sets the laws and standards for their facilities.

They do have the option to pick up option that has less attached taxes. Or not to buy something.

Who imposes the taxes then? The exporting country (China) is unlikely to do it. The importing county is only likely to do it if the government and people support it. The problem is that even with a tax on the import, polluting in a developing nation would likely be cheaper than not polluting anywhere else. Many items do not have options to buy from various countries (economies of scale usually consolidate factories and leave little room for competitors). Not to mention that drastically reducing consumption (your comment about not buying) will cause most economies to fail since we are consumer based.

Make taxes big enough to make pollution too expensive even in cheap countries?

Buying less, but more expensive because of less polluting manufacturing methods is the answer. Economy will still keep going.

"Economy will still keep going."

How so? If you are adding crushing taxes, then you're likely to see a downturn in production and consumption, which generally results in a weak or shrinking economy.

Polluting taxes will promote spending on less polluting ways to manufacture. Or better quality goods that put out same amount of pollution, but you end up buying them not as frequently.

Let's take a hipothetical sweater as an example.

Now I buy a €20 sweater every 2 years. Let's say pollution tax would be €10. Suddenly it becomes €30 sweater and my €10/year sweater budget becomes €15/year. Instead, I could buy a nice sweater for €40 (+€10 tax) and wear it for 5 years. Now I'm back at original €10/year budget.

Economy wise, most of the chain is now just making nicer stuff that takes more resources. Aside from truck driver. Who is now moving twice as much sweaters. But €10 tax ideally would go to environment-improving projects and some drivers will make a living in those new sectors.

To a certain extend, absolutely. Much of the richer EU states cause and have caused quite a bit of pollution and without a serious shift in consumption, I don't believe we can achieve our goals.

However, industry is without a doubt a massive resource user. Modern methods in manufacturing can save significant amounts of energy, water, and more. As China is the main producer in many instances, a change also needs to happen there to go from heavy polluting to less polluting methods.

it's the same thing, the tax increases the price for the buyer.

At the end of the day, it's always "user pays".