That exists, ion exchange resins can remove all the salt from water.Something similar to this: https://www.amazon.com/Capacity-Replacement-Softener-Resin-Crosslink/dp/B06WGRJKTS/ref=pd_sbs_4/134-0992469-2003311?pd_rd_w=wdqwH&pf_rd_p=180628c6-6f13-4dbf-9213-f09cdedc7815&pf_rd_r=NRCN3X3JXGFRQAK3D674&pd_rd_r=7dea7b0e-f4ab-46e1-ac88-b024cfe57579&pd_rd_wg=kfUgd&pd_rd_i=B06WGRJKTS&psc=1
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Whether they are cheap heavily depends on the scale, since recycling them is more difficult than desalinating seawater.
But for small-scale 1-10 liters they are a very simple and cost-effective solutuion.