Consider a simple op-amp in a feedback configuration. You can consider the op-amp to be dominant pole compensated and approximated as a first order system.
Let's say that the transient performance (mainly rise time) in response to an input step of the closed-loop system is too slow.
The first option I have is to increase the bandwidth (and drop the gain, maintaining a fixed GBW) and this will make the system faster.
My question is: Will increasing the DC gain help the transient performance? I know it will reduce the BW. But intuitively, it makes sense right, a large gain means the op-amp can react more aggressively in voltage levels to bring itself back to steady-state