Miniaturization of MOSFET vs. Resistors
The resistance of a resistor is proportional to it's length, and resistivity, and inversely proportional to it's width.

The smallest (cheapest) way to make, on silicon, a narrow isolated resistor with high resistivity, is to control the resistivity by controlling the number of electrons/holes, and to pinch the width of the resistor by applying an electric field to the region.  

When you make a structure like that, it's called a "MOSFET". The Metal is a conductor at the edge of the resistor, the Oxide is the isolating region around the resistor, the Silicon is the controled resistive region, and the Field Effect controls the size of the resistor.

If you are making a structure that already includes some MOSFETs, then you've already got the material to make more MOSFETs. Adding a different kind of resistor would not only be larger, it would add more process steps, be more expensive, and probably mean you couldn't make your other MOSFETs as small and cheap.

If you don't use a Field to control the size of your resistor, you will have to make a much bigger resistor.