High resistance, no current. What's the point of a potential then?
Not every gate needs current for it to operate. MOSFETs are an example of voltage controlled devices whereas BJTs are current controlled devices. 

A high input impedance means that no significant current will be drawn and as such components can be chosen accordingly. It also means that the voltage between the divider won't change according to current draw because no current wil be drawn. As such it is safe to use a voltage divider to get a wanted voltage.