One major reason for the classic FBI tilt was that the FBI taught using the crouch stance in which the shooter goes into a crouch position.
With the body in a crouch, the holster is well positioned for a better draw.
I once watched as a local FBI agent taught some deputies back in the 1960's.
He demonstrated lifting the left leg, moving it a couple of feet to the left, then just squatting.
This tilted his upper body forward, which put the FBI tilt holster in a perfect position for the draw.
The FBI tilt also works well when sitting in a car and conceals better then an upright holster.