Compensation allows one to use more BW available in OpAmp
by keeping it stable, so it does not increase the intrinsic BW of
the OpAmp, as Dick points out, just allows one to use more of the
available BW w/o going into oscillation.
Capacitive loading, stray C at OpAmp inputs, all contribute to
instability, and have to have compensation applied unless internally
comped.
There are OpAmps comped internally to be unity G stable. Or comped
for some fixed minimum G, like G >= 10, used at less that 10 will oscillate.