It's obvious a matter of a risk assesment and deciding 'where to draw the line'.
Rally and racing drivers do, of course, where crash helmets, in addition to all the other safety factors built into their cars.
In terms of ordinary cars/drivers, you might argue that it is "taking things too far" to have seat belts AND air bags AND crumple zones AND collapsible steering columns/wheels etc etc. - but I don't think many people would argue that! Perhaps more relevant to the context of this discussion, if it were known that there was a significant risk that, under certain circumstances, one of those safety features might 'fail', that would be an argument for having others (as 'belt and braces').
I think your premise may not be totally correct. I would say that the armour of SWA is "designed" to provide mechanical protection and also an earthed sheath that will facilitate operation of a protective device in certain situations of cable 'penetration'. It so happens that the armour is usually (but not always - see our wiki) electrically adequate to be also used as the cable's 'earth' conductor - but I would not personally say that it was "designed" to have that role.
However, as has been said, you are right that the armour alone usually is adequate, and compliant with regs, and that a good few people believe that is the appropriate and 'correct' way to do things. However, as I said earlier, the only advantages of doing it are slight benefits in terms of cost and convenience - there is no electrical reason for not having an 'earth' core.
Kind Regards, John
Regards, John