Ophiolite
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Reading through the third of the links I was interested to learn that, in addition to salt, some substances are already being extracted from sea water. (Comments below, in italics, taken from the link) It seems the answer to the OP is "mineral extraction is affordable now and is practised. However, it is not widespread."
Bromine:
Large quantities of bromine were extracted from seawater in the early to middle 20th century using the ‘blow out method’.
Magnesium:
There are several forms of magnesium that have historically or are currently being extracted from seawater including magnesium metal and various magnesium compounds. Magnesium metal was once predominantly produced from seawater . . .there are a number of facilities around the world that produce magnesium compounds from seawater including facilities in Ireland, Japan, Norway, and the USA.
Potassium:
Potassium compounds are currently produced from seawater as a byproduct from solar salt operations, which makes up a small percentage of worldwide potassium compound production.
Bromine:
Large quantities of bromine were extracted from seawater in the early to middle 20th century using the ‘blow out method’.
Magnesium:
There are several forms of magnesium that have historically or are currently being extracted from seawater including magnesium metal and various magnesium compounds. Magnesium metal was once predominantly produced from seawater . . .there are a number of facilities around the world that produce magnesium compounds from seawater including facilities in Ireland, Japan, Norway, and the USA.
Potassium:
Potassium compounds are currently produced from seawater as a byproduct from solar salt operations, which makes up a small percentage of worldwide potassium compound production.