small signal analysis is used to get Bode plot, you can get the loop stability information and BW (speed) of the loop. Time domain simulation is also important.
OP operates at big signal at its output, you will always connect the OP as close loop (with beta). Small signal analysis will tell you the open loop GBW (open loop Wu ( A(s)x Beta`s ) 0dB frequency in Bode plot ) = close loop -3dB frequency (= 1/time constant) ) & stability information about the close loop circuit. Time domain verification is also important such as step response. OP is usually work at big signal (in designed swing), but not small signal. Small signal analysis is a very good analytical method. But it can not tell you about the SR.