Remineralization is a well known and solved problem in existing processes (RO and distillation). I personally built and ran a high performance RO that produced < 5ppm TDS water on my farm, and experienced the ill effects of drinking demineralized water. Excess thirst, urination and muscle cramps.

The WHO published an excellent study on this issue. The issue is not an actual lack of minerals, as we get very little of our minerals from water, but the fact that your body is not designed to absorb water with zero solutes. Effectively the sensors in your gut go out of span and you end up dumping solutes from your bloodstream instead.

The solution is very simple and cheap, that is to add any salt so that your body can detect it. Sodium chloride is fine, being "normal salt" of course, but I add potassium chloride as most of us get too much sodium as is. This is available as "salt substitute".

A pinch in a glass or a tablespoon in a 5 gallon jug is enough to completely eliminate any ill effects. Commercially as mentioned you can blend back some of the brine stream. It's not really a problem as long as you don't effectively deliver DI water to your customers by accident.