But nowadays private interests can cross international borders with ease, while governments cannot.
It was nice dealing with you. I hope you don't mind if I mention your name at the press conference we'll call soon to announce signing of the deal for our new plant with your neighbour."
There's no bribing involved in this scenario. Just plain market competition at nation-state level.
Why not? Constituents like it because it brings back the jobs that left because moving them out allowed companies to avoid environmental regulations, which they can now not avoid either way if they want to sell in your country and so might as well bring the jobs back.
If it succeeds.
I guess you could do that; a sovereign state can try whatever they like. But has that ever actually happened? I can't think of any case where a country banned import of a product on the grounds that its manufacturing isn't up to environmental standards, even though the manufacturing happens in a different sovereign nation, and is compliant with that other nation's standards. I imagine trying to do that would quickly escalate the issue from business to international politics.
If the EU tells you you can't produce anywhere in the EU because of how dirty your factory is, you can still produce it in the US or Russia and then ship it to the EU. However, your supply lines have just gotten more complicated, expensive, and error prone (because of distance) - so that's one part of the equation that a company has to take into consideration as well.
On top of that, I'm fairly sure there are quite a few Europeans who will applaud politicians who stand up against polluting or otherwise unethical companies, and who look down on (and not vote for) politicians who do shady deals with polluting companies.
So, as always - it's not so simple, and there's more than one dynamic at play.
Edit: I am getting a lot of down votes so let me clarify: if external costs are not internalised, humans will ignore it.
Internalising the cost does not even need to mean tax. Many clothing brands in my country, even the budget brands (think Walmart), have been pressured by consumers into using more ethical factories. The same could be done by forcing companies to disclose what factories they use and the factory carbon footprint.
I don't understand what your solution is. Ban importing goods? Tax imported goods based on factory pollution and standards?
"All governments taking responsibility simultaneously" is not something that ever happens. And even if it did, in a moment of selfless reflection of all global leaders, weaker economies will still have a powerful incentive to relax the standards to compete better with stronger economies. I don't have a solution, I'm just saying how things are. Restricting the ability of multinationals to play countries against each other would help in this matter, but it would probably gum up the economy too hard to be worth the attempt (not to mention, it would have to be another thing most governments would have to agree on simultaneously, otherwise the ones to attempt it immediately lose).
The overall point is: it is a tragedy of the commons, just not a local one - an international one. The solution to tragedy of the commons is to have a higher authority unilaterally force participants to limit their use of the commons. But we don't have any higher authority above nation states, so we're ill-equipped to solve tragedies of the commons at international level.