You are not the only one to argue that only a group of countries adopting carbon taxes might not work in long run. Here's an extended comment on that:
These international negotiations have so far failed to deliver any more than ‘roadmaps
for agreement’. There are now at least three ways to proceed for countries or regions
aspiring to leadership, such as the EU:
(i) maintain the current, largely unilateral policy regime, risking carbon leakage
until a new global deal is implemented in 2020, and accepting major economic
inefficiencies and increases in global emissions consistent with likely temperature
increases above 2 degrees C;
(ii) accept that the current regime leaves little chance of achieving the 2 degrees C temperature target, and extend exemptions from domestic carbon prices (e.g. the free allocations in the EU ETS and Australian Carbon Price Mechanism) and other implicit
subsidies to the export sector to protect domestic industry as the world warms; or
(iii) apply BCAs to countries that have not taken ‘equivalent measures’ to internalize the carbon externality.
The current EU approach is largely focused on protecting its own industries from carbon leaking through an extensive CLL (carbon leakage list), which provides 100% free allowances for the sectors on it; and this list is pretty extensive...
Sectors must meet either one of three quantitative criteria to
be added to the CLL (carbon leakage list). Even if the quantitative criteria are not met sectors or subsectors
may be added to the list following an assessment based on three qualitative
criteria (European Parliament and Council (2009), art. 10a (17)).
167 sectors, and in some cases sub-sectors, were added to the CLL based on the
quantitative criteria, of which 10 meet more than one criterion: 24 sectors meet
criterion a), 6 meet criterion b), while 147 sectors meet criterion c). 6 sectors were added based on the qualitative criteria.
In trading Phase III (2013-2020) allocations to installations in sectors not deemed to
be at risk of carbon leakage are adjusted using an allocation factor such that they
received 80% of their original gross allocation in 2013 for free, decreasing to 30% by
2020 (Directive 2009/29/EC, art. 10a (11)). However, if a sector is on the CLL
installations continue receiving 100% of the original gross allocation for free.
(And since you mentioned it, steel production in on the current CLL. For the current ETS troubles of UK steel manufacturers see this more specific question; it's Brexit related.)
The last measure mentioned in the first source (Border Carbon Adjustment tax) is certainly more controversial and hasn't been adopted insofar as far as I know. It also goes by some different names such as "Border Tax Adjustments (BTAs)",
John Hontelez, secretary general of the European Environmental Bureau (a federation of 140 environmental organizations based largely in European Union member states), made similar points in a widely-circulated piece from April 2007, "Time to tax the carbon dodgers". He wrote:
Border Tax Adjustments (BTAs) might be the answer which allows the EU to develop responsible climate policies without having to wait for other countries. They would result in products imported from the US being taxed to compensate for resulting differences in production costs. Thus EU firms would be protected against unfair, carbon-careless competition from outside.
The EU seems reluctant to start a trade war with... well most countries on this... including China, India, and the US (over there, there are some state-level schemes, but not federal ones.)
It looks like the French favor such a border carbon tax but the Germans and Nordics do not.
Already defended by former French Presidents Sarkozy and Hollande, the idea of a carbon tax at the EU’s borders is typically French and has ended up convincing almost everyone. [...]
But a lot needs to be done to convince European partners of a ‘green protectionism’ with a French touch. In Germany, the conservative Union of CDU and CSU expressed their opposition to a national carbon tax, defending the reform of the European carbon market instead.
Sweden also appears viscerally attached to free trade, as even its representatives from the Green party refuse to introduce obstacles on the all-powerful market.
Not surprisingly, Germany has a large export sector, most likely to be hit by retaliations in a trade war...
There's actually a 2015 (French) paper that tried to estimate the impact of EU BCAs and thus retaliations it could face. In the worst case (if EU taxed indirect emissions), China, Russia and the US would all have retaliated with 2-2.5 bn dollars each, and India with around 1 bn. Most of these retaliations would have likely hit the EU agrifood business in their opinion (this was a pre-Trump paper, so German cars etc. were not on the map then.)
There's also an official answer from the Commission in response to a MEP inquiry, in 2017
On the contrary, the design and implementation of a carbon border tax would be extremely complex, with high administrative burden, raising issues with regard to the compatibility with the rules of the World Trade Organisation. Consumption-based accounting of emissions, including non-EU products, raises large technical challenges at this stage.
Some Commission-affiliated economists have actually published a longer analysis of possible BCAs, which mostly echoes the Commission's skepticism, but this paper also found that some simplified variants may be feasible, e.g. using data only on sectoral emission by region. (Interestingly, they had a Spanish but not a direct EU grant to study this.)
Also China (paper) launched an ETS scheme on Dec 19, 2017. In theory:
Under the initial scope, the ETS will cover 3.5 billion tonnes of carbon dioxide from 1700 installations, accounting for over a third of China’s total carbon emissions. This means that China will overtake the EU, which covers 1.4 billion tonnes, as the world’s largest carbon market.
Many details about the Chinese ETS are yet to be decided and announced. This includes the initial level of the emissions cap and its planned trajectory over time.
Given the list of pending tasks, it is not yet known when trading will begin. Experts expect the set-up of the ETS to take at least one year, with 2020 likely to mark the launch of actual trading and broader sectoral coverage. This would coincide with the publication of China’s next Five-Year Plan and the submission of its new climate pledge under the Paris Agreement.
Once fully implemented, the Chinese ETS is expected to cover around five billion metric tonnes of carbon dioxide. According to a report by the International Carbon Action Partnership (ICAP), this means that 15 percent of total global emissions will be covered by carbon markets. Experts argue that China’s national ETS can spur wider climate action around the world.
So its effectiveness remains to be seen. Insofar there are some concerns that China is not releasing enough company-level data to allow for independent verification of the effects of their carbon policies. The Chinese only allow select[ed] people to receive this data, unlike the public disclosures in the EU, for instance.
But (for now) the initiation of the Chinese ETS bolsters the claim that leading by example (as the EU has done) is better than imposing border carbon taxes.