Resistors in a differential amplifier must have accurate values that do not change. A transistor has a variable resistance that is also changed when the voltage, current and temperature are changed.
I understand that mosfets might take the place of a resistor, when etching integrated circuits on a silicon wafer. The small size of mosfets makes extreme miniaturization possible.
To obtain a particular resistance, the designer would need to know the exact properties of the mosfet. Also how to combine them. There's N-type, P-type, enhancement mode, depletion mode, etc.
I have never designed an IC but I understand that they use a physical ratio, not actual resistor values to make accurate voltage dividers. Maybe the physical ratios of transistors can also make an accurate voltage divider and since they are close together then their temperatures will be almost the same so their resistance changes when the temperature changes will cancel.
One important aspect for using bipolar transistors as a replacement for ohmic resistors is that you only can realize differential (dynamic) resistive units for samll-signal operation (large values in the higher kOhm region).
Therefore, if you want to realize (controllable, variable) ohmic resistors using transistors you must use FETs.