I like to know what the citations are as I read and prefer parenthetical citations. Personally, I find number citations highly disruptive to actually use, since I need to flip to the references every time if I want to understand what they refer to. Why do prestigious journals [1, 2] use numeric citations? Is it simply to reduce word count?
References
The citation style is a matter of personal preference.
proof: I prefer the numerical citations (especially if they are in superscript). Numeric citations are easier to skip, allowing me to focus on the content of the paper. I find the long author-year citations in the middle of sentences and paragraphs very disruptive because they take up space and force me to search where the sentence or paragraph continues.
I believe the advantage is mainly shortening the text. This can be substantial in some cases. If a short paper wants to mention 20 studies, then often the references can be reordered so that the reference looks like [3-22] instead of several lines of text listing all the first authors.
For longer papers, this reordering is not usually possible, so [3-22] is followed by [3,4,5-7,40]. Also, the cost of flipping to the end of a longer paper is higher.
I can live with this style. What I hate is when titles are dropped.
I think there are a lot of good answers already, so this is superfluous, but it sums up my sentiment:
If I have numerical references, I can easily skip them when reading a paper and I can easily find them in the bibliography. They are also easy to note down on a piece of paper. It is easier to find reference 124 then to search for a name in a long list of authors... - Add to that, numerical lists are typically created by tools while some authors insist on handwriting author-year references. Great if the reference you are looking for doesn't exist...
The author-year reference then brings along the issues mentioned by other contributors: Does it become part of the text or it is a label? If I write it as if part of the text it impacts the writing style. Then how do I add a long list of authors?
And as others have pointed out, whom do you list? The first author? (The robust approach) or the group leader (recognizable name). My personal BibTeX libraries are internally author-name(-a/b/...) which works, but means you are potentially referencing a "nobody". This then might even impact reader interaction where you will be more attentive to a recognizable reference than an unrecognizable one which is objectively obviously wrong.
So numerical references provide a wonderful opportunity to attribute work neutrally in the written manuscript.
And on a comment to other responses: I agree that references without titles are problematic as most papers can be found with a title and an author, but random jumbled number with cryptic abbreviations are sometimes wrong and universally harder to find... (Even worse if the literature of interest spreads over a wide field of journals and sub-disciplines....) Fortunately "digital paper" is cheap and modern papers are no longer impacted by the inherent cost of printing physical books, so this is less prevalent than in the past. (Though still an issue...)
Well, this is probably one (yet unmentioned) reason for doing it - however, it usually makes sense not for journals, but for academic graduation papers like theses etc., since many of them impose restrictions on the total count of citations used. (For example, in one of the Russian universities, the formal requirement for a postgraduate thesis was (as of 2021) using no less than 120 references.)
Using numeric style, the task of complying with these requirements is easier for both the author and the verifier. Otherwise, the bibliography should at least still be kept in a numbered list (or should we employ manual counting?).
Another minor reason is that numeric citations are unambiguous, while "author-year" ones are not (it is not uncommon to cite several papers written by the same author(s) and published in the same year (maybe even in the same journal)).
The main benefits are:
The latter is especially important for graduate students who might be afraid to consider ideas in conflict with those of established researchers.
The other answers here discuss the benefits of numeric citations, so I'm going to mention a drawback of this style (compared to author-date style citations). Sometimes when you're reading a paper, it's nice to see the historic progression of the references, to get a sense of how the subject has developed over time. This is particularly useful for a literature review or history of the subject. In such cases the numeric citations are annoying because you don't get to see the years of the work as you read through the discussion. (You have to keep looking back and forth at the references to get them.) Contrarily, if you use author-date style citations then this gives the reader chronological information as they read through your work.
The author's text should explain their argument. That means their text must (or at least should) state their starting point facts or postulates, and then move from those onto their own work which builds on that base. If you need to know what "Ref123" is about in order to follow the author's reasoning, then the author hasn't written their text well enough. This is something that their reviewers should feed back on before it gets published.
Of course the author can assume the typical knowledge of the field and terms of art. But anything more specific to their work needs to be stated explicitly in their text.
Where references matter is for people who want to check that the starting point facts or postulates are actually correct, that the author is using them correctly, and that there aren't implicit assumptions which would cause problems. If you get to the point where you're checking this though, then you've already absorbed the author's work to the point that cross-referencing will not be a big deal by then.
