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I am quite surprised to find that a lecture slide for a course has 133 citations from highly reputable researchers across the world. The main contribution of the lecture slides (which seems to be the reason for the citations) appears in 1 line on 1 page of the slide out of 30 slides.

https://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf

To see citation count, google: "RMSProp"

Another set of random course notes from lecture 12 of a course just happens to have over 100 citations

http://cs229.stanford.edu/notes/cs229-notes12.pdf

Google: Reinforcement Learning and Control - CS229

This 8 page course note has 200 citations, which is more than many of actual research papers

http://cogprints.org/5869/1/cnn_tutorial.pdf

Also, another summary of a blog post (less than 14 pages) have over 700 citations (From the paper: This paper originally appeared as a blog post at http://sebastianruder.com/
optimizing-gradient-descent/index.html on 19 January 2016.)

https://arxiv.org/pdf/1609.04747.pdf

To see citation count, google: "An overview of gradient descent optimization
algorithms"

This paper isn't even published anywhere aside from Arxiv.

What is the point of even publishing a paper and going through the painstaking process of peer review and editing if you can just write some blog post or a power point lecture slide on some hot topic and accumulate citation counts (which is crucial for securing funding, etc.)?

It's not fair to only look at the peak of the distribution. For an apples-to-apples comparison, you need to compare peaks to peaks and averages to averages.

The two sources you mention are both in the field of machine learning. If we assume that they correspond to the blog/lecture notes sources with the most number of citations (i.e. the peaks), then we can conclude that these venues can generate at most ~700 citations. If you compare to the most cited machine learning papers, these 700 citations are minute. For example putting "machine learning" into Google Scholar yields:

Scikit-learn: Machine learning in Python (journal article) -- 14919 citations

Data Mining: Practical machine learning tools and techniques (book) -- 34724 citations

What about averages? I don't know what the average number of citations a blog post or lecture slide gets, but I'd guess less than one, since many blog posts don't attract comments. The average number of citations for a journal article however is easy to find - just look at the impact factor. Putting in "machine learning journal" into Bing, I get journals such as Machine Learning (IF = 1.855 as of time of writing) and International Journal of Neural Systems (IF = 4.58). Clearly the average journal article gets a lot more citations than the average blog post or lecture slide.

tl; dr: What's the point of studying machine learning instead of playing soccer and earning hundreds of thousands of dollars a week? The answer to that question is similar to the answer to this one.

1. The instances you mention don't show that statistically blogs or slides get cited well. Just that you find some instances in the universe of events.




2. Papers tend to be abstracted (chemistry does this quite well). Blogs and slides not.




3. Science citation searches don't generally index blogs and slides (especially uncited ones). Thus they can be difficult to find during a lit search.




4. Journals exercise a function of review and editing that drives a superior work product in formatting. Blogs and slides are generally a mess in their referencing fro instance, compared to papers. It's not just that editors and reviewers drive this but that authors tend to "up their game" when sending work product for review.




5. There is some benefit in review scientifically (more so for weaker papers, but still).




6. Papers help your career.




7. Nothing prevents publicizing a paper by blogging or presenting it in addition. And usually the blogging or presenting will be superior because solid work has already been done previously.*




8. Narrative technical reports ("Word documents" or the sort) are generally superior to slideware in information density and quality. [Read the Tufte contributions to the Space Shuttle disaster inquiry for some of this...Feynman had same issue with the previous disaster and the problems with slides versus sentence and paragraph reports.

*Small aenecdote to explain. I took a course once where we had a true seminar (oval table discussion with small group) on foreign policy controversies. Every Tuesday, we handed in a 2 page written paper before the discussion (on a set of readings). Every Thursday, we just had discussion, on a new set of reading, but no paper was required. The Tuesday discussions were stunningly better than the Thursday discussions. Doesn't this make sense when you think how much better you understand something after writing it up properly? The same applies for doing a presentation or a blog on a piece of science (after writing it up formally).

The principal contemporary reason for formally publishing articles is that governments and institutional administrators demand of researchers proof of their productivity. Being unable to assess such productivity according to their own criteria (in general because they have none) they attach simple metrics to research activity which they use to rank researchers. The principal metrics are money secured in competitive grant programs and counts of papers indexed by some supposed authority. In the current moment, publishing in journals serves mainly to achieve the second goal.

Formal journal publishing generally adds little value from an intellectual point of view and generates obstacles (paywalls) to dissemination of ideas. Something like the ArXiv achieves wide, free, dissemination of knowledge in a rapid and easy way. The author can write an article according to the author's criteria and distribute it as the author sees fit. Sometimes the refereeing process adds value, when the referees and editors behave in a serious fashion, but more often they do not or the process simply delays dissemination.