it consists of unloading fx, but it would include muting items and their automation indeed. So it could use a separate button. I thought about reusing an existing icon though, because not many people would put track offline, and still want to enable their fx, and the mute switch could be saved for "quick mute" that could be automatable (as in McLogic).

Mute, FX Off, FX Offline. Select all on track and mute. hmmm Could be something else. I quite like the deactivation of tracks in Protools. There is made sense because of limited DSP resources. Here it would make stuff easier perhaps. A hard mute would OFFLINE the fx and kill the channel. +1 for hard mute

+1 for hard mute absolutely :).