It seems rather inefficient for the batteries to be shipped overseas and for their materials to be extracted by 10 year olds, rather than to just have the batteries be recycled in the country where they are used.
Car parts are overall more expensive, and installation, replacement and even disposal happens through specialized entities, typically. Most maintenance work is done by manufacturers or dealers themselves.
In other words, it's not inevitable that car battery systems would necessarily be sent overseas the same way that consumer electronics are when they reach end of life. With lower volume and more centralization, regulation will be easier to implement and enforce. And the economics may also make it cheaper for initial recycling to be situated in the originating country as well, given that the parts are more valuable and given the economies of scale that emerge from centralized reclamation networks.
Already in the US there is a healthy industry of third-party businesses that will replace hybrid car batteries and reclaim the old systems for refurbishment. Most of the reclaimed systems are refurbished and re-used.
There's no reason to think that with proper regulation and standardization an efficient & environmentally-safe reclamation market cannot emerge in first-world countries, preventing car battery waste from spilling over to third-world countries.
More seriously, global shipping at scale is ridiculously cheap. This site currently shows a rate of $987 to ship a 20' container from NYC to Jakarta: https://www.icontainers.com/ship-container/indonesia/