Shouldn't be much different from extracting salt from seawater, which we already do.

We already do it when making salt. We just throw most of the none NaCL salts away.

Lithium extraction is already done from brine, effectively from "fossil seas".

Why? It could be simply done in the countries where there are no eco-nazis, which is most of the world's countries - especially countries in warm seas where it shall be done.

I assume the "eco-nazi" part is why you're being downvoted, but I think your basic premise is absolutely correct. If the Western world outlaw this practice it will just happen in places like China and India instead.

With significantly less environmental oversight and regulations. The pollution could perhaps end up crossing over to western countries at higher levels than any domestic, well-regulated, production would emit.

The other side effect of added regulations is generally that the extraction gets more efficient too in order to maintain higher profits, so it helps stretch out the resource for longer too.

And in a whole lot dirtier and environmentally damaging way.