What kind of person bills his grandmother for taking her to the supermarket? Jeezz...
Repeat after me: "it's against the law to drive people around for money without the proper credentials".
Your bit about "without proper credentials" makes it sound like all that's needed is for a driver to apply for a license and meet some objective requirements like driving records, vehicle inspections and insurance. If that were the case, you'd have a lot more folks siding with the law.
Instead, in order to pick up a fare in Amsterdam, you need to meet some other arbitrary requirements, chief among them being a member of a TTO ("Regulated Taxi Organization") with at least 100 cars. And to pick up a fare from a taxi stand in Amsterdam, you need a further license -- one given at the discretion of the municipality for "professionalism".
So there we have it -- there's a whole set of common sense regulations that are applied and that anyone can meet based on a set of objective criteria. Then there's another set that got "glued on" which makes no sense at all. So ditch the latter, and soon you'll find there's no reason for uber at all.
[ But hey, at least it's not as bad as the US medallion system ! ]