Often a resistive divider has to compete, yet cooperate, with something else.
* One common situation that comes to mind is biasing a transistor. Making a divider using low resistances will drown out your input signal. It will also use up (waste) several milliamps between the supply rails.
Very high resistances will be unable to compete with your input signal, unless your input is also very high resistance.
* Another situation is a gain (volume) control. If the potentiometer is very high ohms, it will cause extreme change within a narrow region at one end.
On the other hand, if you are biasing a mosfet, the pot can be very high ohms. This is because a mosfet input is also very high ohms.