Your comment that there are currently no GPS approaches at commercial airports is not true. Almost every commercial airport has GPS approaches. The are called RNAV (GPS) or RNAV (RNP) approaches. I work in the section of the FAA that designs and develops instrument approaches. The trend is for more and more airports, commercial and general aviation, to have increased RNAV approaches published. They get much lower minimums than conventional non-precision approaches, not as low as an ILS, but pretty close.
What’s RNAV got to do with GPS?
We have had RNAV long before the first satslite ever went up!