Single off-the-shelf op-amps force a trade-off : an IC can either have great DC precision (low offset and drift) or high speed and heavy output drive, but rarely both at the highest levels. A composite architecture gives you the best of both worlds :

High DC Precision + High Output Drive : Delivers microvolt-level offset and low drift while pushing hundreds of milliamps or high-voltage swings into a demanding load.

Wide Bandwidth at High Gain : Splitting the gain requirement across both stages prevents either amplifier from running out of bandwidth as quickly as a single stage would. See also Cascading OPAMPs For Increased Bandwidth

Low Distortion : The outer feedback loop cleans up nonlinearities introduced by the fast output driver.

Stability and Oscillations : Because you are combining two phase-shifting amplifiers inside a global loop (plus any local loops), the phase shift can easily add up to 180° and cause self-sustaining oscillations or ringing.

Frequency Compensation : Designers usually have to add a compensation network (such as a small capacitor across the feedback resistor - R4 in our drawing above) to roll off the loop gain safely and maintain a healthy phase margin.

PCB Layout Sensitivity : Short feedback paths, tight decoupling, and careful management of capacitive loading are critical to prevent instability.

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