I'd agree that it is not widely known. I would also suggest that many of those who do know of it, do not understand it.
An issue is that the use of the word 'tyranny' may come across as aggressive to some. This is because Mill philosophy is focused heavily on individual freedom. To be fair, this kind of language has often been used in political philosophy for more than 2,000 years.
Tyranny of the majority cannot be summarised as being 'mob rule' or 'dissatisfaction with majority rule'. It is more nuanced than that. Rather, it is multi faceted. It's about protecting individual freedom, autonomy and dissenting viewpoints, and the need to have some balance between individual freedom and collective welfare 'harm principle'. To be honest, that explanation does not do it justice.
The use of the term is unlikely to be simply about, "we don't like majority rule".
Based on the facts that I knowing nothing about our submission and very little about our grievance, I would guess that tyranny of the majority is referenced because we are more widely dissatisfied with governance process.
You cannot have a media manager go through the submission and click on the thesauras function and change the word 'tyranny' as that would lead to a different meaning altogether. Our submission was likely put together by an experienced KC. Having dealt with QCs/KCs over the years, who are most likely not as good as those commissioned by the club, I would trust the reasoning behind the use of the phrase.