None
The aim of this site is discussion, and not to apportion blame.
My point is ....assuming the pilot is in control of the aircraft and its systems....that any unauthorised manoeuvre carried out in airspace which requires compliance with ATC instructions may be considered illegal in some nation states' airspace.
If the pilot is instructed to fly an assigned heading to intercept the localiser then it is the localiser and not another form of tracking reference that the pilot should intercept. I believe the original poster meant to highlight that point.
This should not preclude any pilot from asking for approval for any particular manoeuvre at any time.....but please tell or ask first...keep the controller in the loop.....we're not psychic!
What goes through a controller's head?
FMS failure? Unlawful interference? ILS failure? Radar/tracking malfunction? RT failure? Unexpected wind anomoly? Wake vortex upset? Pilot incapacitation?......we watch everything....tell us what you're doing if it is unusual....we're here to help, not hinder.