Just to clarify things a bit, RO filters do remove/lower total dissolved solids (TDS) by having a reject water stream with the extra TDS in it and a purified (permeate) stream with the clean(er) purified water, but for any sort of membrane life, they need to be supplied with softened water.
Water softeners have resins inside that exchange sodium ions for magnesium or calcium. Some resin mixtures can even remove some of the sulfate in the feed water. That means that while the TDS stays the same, there aren't insoluble hard water deposits on fixtures or clothing.
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After water softening, an RO filter (membrane) then takes the sodium, and many other ions 90+% out of the water. Our RO takes out 98.7% of all the dissolved solids, but that is very much a YMMV number as the overall efficiency has a lot to do with what exactly the ions and counter ions are in the feed water, the feed pressure difference, the membrane quality and age.
I used to make ultrapure water for work. There are lots of ways to skin the cat, but lots of variables. Drinking water is pretty easy. Kidney dialysis water is harder. Other forms of pure water can be fantastically hard, like clean water for making semiconductors.
But back to
@etpm's question: I think it is a question of cost and hassle. Buying soft bottle water is low capital, high hassle, adding a water softener and RO is a capital investment, and maintenance commitment (buying salt, changing filters and membranes) and will not fit under a sink, but might be plumbed to give you soft water throughout the house for improved laundry and ease of cleaning, as well as feed and RO unit for low TDS water.
All the best,
Peter