Why is a Instrumentation Amplifier Necessary for A Wheatstone Bridge (small signal circuits)
Yes, the input stage buffers are required so that there is a very high impedance load on the bridge and that the buffer load has virtually no effect on the resistors in the bridge.
The outputs of the buffers are very low impedance (typically less than 0.1 ohms at DC) and so the loading effect of the differential amplifier (inside the InAmp) has negligible effect.
There is a voltage drop across R2 and R3 because that is how a differential amplifier works but those resistors do not load the output from the buffers and cause an error.
Connecting a diff amp directly to a Wheatsone bridge will always cause errors that are circumvented by using buffers.