We buy our toothbrushes from a retail store, many transactions removed from the manufacture of the toothbrush, and every organisation in that chain would have to voluntarily agree to honestly report its transportation details. This is unlikely.
Even if it did happen, the onus would then be on consumers to interpret these details, perform a comparison between a number of available brands, and determine the most conscientious choice. And then review this decision periodically, because transportation contracts come and go. This is a substantial amount of work.
Even if consumers were able to do that amount of work, they'd then have to replicate that work for every single product, because everything goes through a similar transportation process. There is absolutely no way that any individual has enough time in their lives to research the transportation details of even a reasonable sampling of products used.
And that's not even considering the transportation issues in the supply chain!
As you observe, individual organisations also cannot act, because doing so makes them less competitive.
This is basically the same reason why individuals can't effectively tackle climate change. There is far too much information that's hidden, and far too much time required to effectively assess information, for individuals to influence anything.
Like with climate change, there is a solution, and it's regulation. The problem would vanish overnight if the EU, the US, and I guess now the UK all refused to allow docking of ships with flags of convenience, or even just ones flying flags from countries that don't ratify the maritime treaties.
And like with climate change, the solution is hampered not because of technical difficulties or cost, it's hampered by lack of will to spend a relatively small amount of money on something that only has a social good and not an economic good.
