There’s nothing inherent to leadership or uniforming that makes people prideful.
I have to disagree with that statement about leadership, but not necessarily about wearing a simple uniform that generally resembles contemporary attire. I think the notion of the OP has merit, and is for all intents and purposes not merely a vice based in the individual. If someone would like to speak in absolutes about this, then I think you have a point that virtues and vices are not necessarily inherent to any role. But I think the OP’s intent is not to speak in absolutes, but is instead speaking of human beings who are subject to concupiscence in a real world environment.
I think leadership roles have the inherent pitfall of pride built into them. Some people are attracted to leadership roles for no other reason than to attain status and admiration. There is a reason that people who crave those things seek them in leadership roles.
Simple uniforms are one thing, but I suspect the OP is referring to regalia, or such things that appear to be unnecessary regalia, such as cassocks, mitres, and tiaras. Having leadership put on flamboyant attire is an invitation for pride to attack the leadership, and an invitation for envy to attack the weak.
A few of the more recent popes felt the need to do away with unnecessary regalia and ceremony…the papal tiara and coronation, for example. Pope Francis takes those initiatives to heart by attacking clericalism within the Church.
I can tell you from experience that pride and ladder climbing are inherent pitfalls to leadership roles, or conversely, inherent perks to leadership roles, depending on the vice or virtue of the individual who takes such a role.