One has a lot of meanings, it can also be used to enumerate lists of examples.
In this case, the sentences imply that there are many reasons for why someone would do whatever is being discussed here and they are explaining what those reasons are.
So, when you write it this way, "one" is referring to whatever is being counted. The writer is using "one" so that the subject doesn't get repeated. Saying the same word many times in a row is discouraged in English writing. So, what this is actually saying is:
The first reason is [a/the reason] of brevity.
The third reason is [a/the reason] of content.
Using "one" in this case is emphasizing that "brevity" and "content" are reasons, in the sense of: "reason of brevity" and "reason of content".
If you shortened it to:
The first reason is the brevity.
The third reason is the content.
This doesn't actually show that "brevity" or "content" are necessarily reasons. They also aren't complete thoughts.
Let's look at an example:
I like to write using the writing style called X. There are three reasons why I like it:
- The first reason is one of brevity. Style X focuses on succinct and concise writing that conveys the information without taking up a lot of space.
In this case, it's clear that brevity is a reason that I like the style, and I explain it more in the following sentence.
- The first reason is the brevity [of the writing style]. Style X focuses on succinct and concise writing that conveys the information without taking up a lot of space.
In this case, without the part in brackets, the sentence doesn't feel complete.
It's difficult to say which is more appropriate in this case as you've not included more context but I would tend to side with the intentional use of "one".