The bottom line is:BS 7671 doesn't say you can't.
It doesn't say you can't walk up to someone in the street and stab them with an earth rod either but are you going to do it? Deviation only means no defence if needed.
No-one on this forum has offered a valid (electrical) reason why you shouldn't.
An additional earth path can only make the installation safer.
How can you say that? What proof have you got? Its a deviation from 7671 so, again no defence. What about the fire thats started as you only put a 4mm cable on the earth rod and it tried to push the pfc though it and it melted?
Ze won't change - the main earthing conductor (MET to cutout) is disconnected for this measurement (no rod).
Well thats wrong as YOU have installed it as an earth path so should be left in.
Zs will be better (rod included)
Should the dreaded happen - loss of supply neutral - then you have an alternate path for the current to flow.
And this is why it should be at the PEN as you may well get all your neighbours too!!!
That's the arguments for - what have you got against??