Excuse my ignorance but then, what do you need a church leader for if you can just read the words right out of the book?
I think the original rationale was rooted in a couple different things:
1) many in those leadership positions actually get theology degrees (meaning they were able to put aside an amount of time to study the materials that an average person wouldn't have
2) when many of these positions were founded/formed, illiteracy was a massive issue, so even a person had the time and motivation to want to learn it for themselves, they lacked the ability to do so.
(and even when reading rates started to improve, they ended up opting to use only Latin as the official language for a lot of it -- keeping it out of reach of even more people)
For those who recall, that was one of the big catalysts for the protestant reformation. Martin Luther wanted the texts to be available in the vernacular (common languages) so regular people could read it themselves, reducing the Catholic church's control over biblical interpretation.
I've used a software analogy in the past, I would imagine I would be considered a pretty important guy (and would wield a certain amount of power) if I was the only one in an entire city who knew how to write code. If I caught a whiff that some others were trying to learn to code so they could see what the app was doing, and I intentionally converted it over to use an obscure programming language, and hid the copies that were in an "easier to interpret" language, that would be even more dubious.
Human nature is what it is...when a person (or people) get certain positions of power/prominence, they're not terribly eager to part with it and go back to being "just a regular guy among many"
How that ties in to present day, it's the people willingly keeping those positions in a status of prominence, not because they actually revere the position, but because it provides an 'authority to appeal to', that can be selectively invoked, as a convenient counter-balance to other forms of authority they disagree with.
For example: People who disagree with their own country's policies on immigration may toss in the "even the Pope says XYZ about immigrants" in hopes that it'll change the opinions of others to one that may more closely match their own.