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This is actually specific to mathematics. In particular, in the sub field of category theory, differential geometry, algebraic geometry.

Question is as mentioned above.

How much is too much when it comes to diagrams in a research article?

Do more diagrams annoy a reader?

I did not expect this question to create so much confusion. May be some one who has experience (don’t ask how much) in reading research articles in mathematics (pure mathematics, if that makes some difference) can say something relevant as it differs from one field to another field.

That entirely depends on the article itself. In some cases diagrams aid an explanation and make it clearer. In others they offer little insight. If an article depends on having many diagrams of the former kind, then I don't see that "too many" is an issue. But even a few of the latter kind may just get in the way of understanding.

Words and pictures can be complementary. It is a judgement call by the authors as to which is best in a given case. They may err a bit, but that is human nature.

In general, think about whether words or pictures/figures better convey your meaning and act accordingly. Sometimes both are needed. Examples illustrating (note the word) a concept are often best presented in figures. Imagine a Calculus textbook without figures. Now imagine one without formulae. Would either work?

I looked at 5 papers of mine in experimental science. The results:

As you can see, it's about ~1-2 figures per typeset page. I did count "panels" (a), (b), etc. as separate figures even though not numbered that way as they are separate on the page.

I never got any push back or even questions on figures from journals or reviewers. Had one co-author on D ask me to pull 3 modeled regressions (or number would have been higher). But the objection was not visual impact but just that he disagreed we needed to show a negative relationship.

In terms of what to show, they were almost all just data graphs and are in the results section. Maybe once or twice I showed a "cartoon" in discussion. Intro, methods, and conclusion tend to be figure free. So the figures are concentrated in the middle of the paper.

I really never wondered what to show--felt intuitive.

I'm assuming by "diagrams" you mean computations done in graphical rather than inline symbolic form. In this case the answer depends on the field and on the reader--some people find a multi-page diagrammatic calculation annoying if it could be expressed more succinctly (if also more opaquely) using standard symbolic notation. However, there has been a general trend towards diagrammatic calculations, so it's a bit more au courant even if it annoys the old guard.

If on the other hand you mean "illustrating pictures," I think it's safe to say everybody likes looking at those.

Personally, I like more diagrams in a paper with good captions.
More complex mental visualization can be aided greatly with diagrams.
If I am skimming through a paper, a diagram will catch my attention more easily, and if the caption does a good job of explaining by itself (with fewer prerequisites from the text of the paper), I am more likely to read other portions of paper in more detail. This is especially true for experimental results. Conversely, not having good captions defeats the purpose of the diagram. My opinion is based on computer science research papers in my small area, however, one of my favorite example is from mathematics

I suspect there will be a practical limit related to experimental/theoretical sciences. You should also consider how peers start to read an article. This will vary a lot, I will often read the abstract first and then take immediately a look on the figures, then, maybe, I switch to conclusion, then, maybe, I start from the introduction. If your results are important and understandable easily, your paper will become cited many times in any way and peers are more inclined to read it, if you present a new method as a unknown researcher, I would apply a poster strategy and think thoroughly about what the 1-2 key statements/messages are you want to present instead of bombarding the reader with redundant figures. The attention span you get is the unknown parameter. Basically, there should be not much redundancy in your paper, therefore the the data/figures IMO should be compressed as much as possible withoug looking cluttered. This is an art and science you have to practice and you should carefully analyse how it can be improved whenever reading other papers. Asking how much figures are too much is leading away from the key problem here, which is attainable attention.

There are fashions in these matters. When I was an undergraduate over 50 years ago, the presentation of pure mathematics was very strongly influenced by the Bourbaki school, which emphasised extreme abstraction. Diagrams were not allowed! If you wanted to study geometry in the two-dimensional Euclidean plane you first should master the geometries in n dimensions (no diagrams possible) and then set n=2.

The reasoning behind this idea, which I must say rendered some of my courses incomprehensible, was that diagrams can mislead.

The question to ask yourself is what you are trying to communicate and to whom. If you know your audience than you will know whether they like lots of pictures or, like the Bourbaki crowd, hate them. If, as is most likely, you do not know your audience, you can bet that what they most want from you is writing, with or without pictures, that is easy to understand.

In short, put in graphics to aid understanding amongst your readers not just to make the paper look pretty.