One of the things the Magistrates or District Judge must take into account is whether alternatives to the defendant driving are available and practical for the duration of his ban. The argument also has to show "Exceptional Hardship", not simply inconvenience. Here's the Magistrates' Court guidance when considering the matter:
" When considering whether there are grounds to reduce or avoid a totting up disqualification the court should have regard to the following:
It is for the offender to prove to the civil standard of proof that such grounds exist. Other than very exceptionally, this will require evidence from the offender, and where such evidence is given, it must be sworn.
Where it is asserted that hardship would be caused, the court must be satisfied that it is not merely inconvenience, or hardship, but exceptional hardship for which the court must have evidence;
Almost every disqualification entails hardship for the person disqualified and their immediate family. This is part of the deterrent objective of the provisions combined with the preventative effect of the order not to drive.
If a motorist continues to offend after becoming aware of the risk to their licence of further penalty points, the court can take this circumstance into account.
Courts should be cautious before accepting assertions of exceptional hardship without evidence that alternatives (including alternative means of transport) for avoiding exceptional hardship are not viable;
Loss of employment will be an inevitable consequence of a driving ban for many people. Evidence that loss of employment would follow from disqualification is not in itself sufficient to demonstrate exceptional hardship; whether or not it does will depend on the circumstances of the offender and the consequences of that loss of employment on the offender and/or others."
If the Duke is successful and retains his licence, the points remain on his licence and he cannot make another argument using the same reasons within three years. Assuming there is unlikely to be another Coronation in that time, he will have to drive carefully.