I think when it comes to costs, the size of the aquarium is a big deal. I wouldn't use this method on my 29g anemone tank. You can just do water changes cheaply. 5 gallons every 2 weeks. Although I do a water change about once every 3-4 months, as it's just anemones and pulsating xenias with 2 clownfish. All those extra elements aren't really needed by the anemone.
However, when it comes to my 180g tank, that's 40 gallons of water change every 2 weeks. 80 gallons of water a month, and now you are looking at salt costs, plus the costs of making the RODI water. That right there is $30-$35 a month, and making all that water is kind of a pain in the butt. Oh, and it messes with my macro values unless you keep them exactly the same as your salt.
And yet the only reason to do it - to replace trace minerals. I have a refugium for nutrient export. I dose alk, calcium and magnesium. The only thing left is replacing trace minerals.
ICP test is pretty much the same as the cost of water change at this water volume. For people with even bigger tanks, it because a financial advantage.
Of course, still gotta pay for the trace minerals to dose, so a little more expensive. But much less time involved and as they say - time is money.