I really don't see the difficulty in understanding. When I post the dictionary definition of 'nominal', you reply "Yes, we know that" but then go on to disregard that definition and state it is arbitrary and irrelevant.
I think you should probably be looking in some 'technical dictionary' or suchlike, rather than a general dictionary. In virtually any other situation in any engineering field I can think of (mechanical, electrical, chemical etc.), as well as in various regulations and legislation about product labelling etc., a specified 'nominal' value indicates the 'average' or 'intended' value of some measurement, usually with a specified tolerance around that nominal value. I can think of no other situation in which (as with UK supply voltage) the 'nominal' value of something differs appreciably from a very high proportion of real-world measurements (and the average thereof) of that something. That is simply not the sense in which 'nominal' is normally used in engineering circles.
It is not arbitrary; it is the same as Europe.
It is arbitrarily the same throughout Europe.
It is not irrelevant; it is the value used for calculations.
.. and therein lies a problem, and a danger, which has only just been (partially) recognised by BS7671. Amd3 at last recognises that using the 'nominal' voltage for calculating the minimum 'safe' Zs for final circuits can result in an 'unsafe' situation if the supply voltage is less than that 'nominal figure' - what matters for such calculations is the lowest possible supply voltage. Apparently because of external factors, JPEL/64 did not require the calculations to be undertaken for a supply voltage of 216.2V - but by effectively requiring calculations at 218.5V they got pretty close.
It is the actual voltage (within the limits) on the day which is irrelevant.
For 'safe' calculations, the actual voltage on the day is, indeed, irrelevant, and some arbitrarily chosen 'nominal voltage' (which could be miles away from any voltage ever seen by the installation in question) is even more irrelevant. What matters is the minimum or maximum 'possible' ('permitted') supply voltage - minimum for some calculations, maximum for others.
How could you have a varying nominal voltage?
In the context we're talking about, one couldn't - which is why it makes no sense to quote the 'tolerance' as a percentage. In other situations, one might have, say, a range of screws (or whatever) with nominal diameters of 3, 4, 6, 8, 10 mm etc.. In that case, it could well make sense to state an acceptable tolerance (for any size) of ±2%, rather than having to quote indiviual absolute tolerances for each and every size.
Kind Regards, John