Why is frequency compensation required here?
Good question!  Your DC analysis is correct, but your AC analysis lacks the frequency effects associated with M1, M2, M3 and M4, including those due to the reverse transfer capacitance.  The phase shift associated with these will vary depending upon which FETs are chosen, but at some frequency your phase margin will be degraded to the place where the circuit will oscillate.  The compensation circuit will roll off the gain before you reach this frequency.