Yes, but, minerals make water less volatile as well as balance it’s PH too.

Demineralised water has, in fact, shown to be highly corrosive to the materials which it passes through or stored in. So, the toxic plastic compounds, in the bottles, may find their way into your drink.....

On top of all this, Cooking food, in mineral poor water, may rid the food of its own minerals. So, this defeats the argument you are giving.

Besides, why shouldn't we be getting out minerals from both food and drink?

One must remember that for every action, there is a reaction. It's logical to believe that by taking out the naturally occurring minerals from water, there will be side effects.

Fortunately, there is also a plethora of research which backs up this logic.