Shock risk; possible inadequate wire size when ICs serve as ground; noise from having ground current flowing through ICs.
(1) If the amp should develop a problem that puts live AC on the chassis, the fault current will be flowing through the IC. Depending on the level of the fault, it may not be enough to trip a circuit breaker, but still be enough to electrocute you (all it takes to stop your heart is a few mA of current). You could be electrocuted from coming into contact with one end of an unplugged IC and chassis of the amp or other component connected to it.
(2) The shield/ground wire size in an IC may not be of a size adequate enough to carry full ground fault current, which can be greater than normal.
(3) Small ground currents flowing through ICs can create the very noise you're attempting to solve by lifting ground in the first place.