You raise good points, but I'm largely with the author.
* grandmothering: The author's examples weren't actually about orienting the paper in the field. They were giving redundant background material on the field itself. I think the distinction was not made clear. If I were to speak for the author, I'd say that it's not about dropping these introductory sentences, it's about making them say something useful to somebody. Orienting a paper's place in the field is useful. Telling me that distributed computing deals with scalable problems is not.
* I have never, ever used the textual table of contents to find my way around. If it was guaranteed that section numbers were included, I might train myself to rarely get some use out of it. If there are no section numbers, it is worse than useless, and sometimes indistinguishable from bragging: "first, we propose a novel algorithm. Next, we prove that it is brilliant. Later, we show how it's what you wish you could have come up with but didn't. Finally, we describe what a loser you would have to be to not recognize our brilliance."
* It may be the opposite of what is taught, but this is the one that I feel most strongly that the author is 100% correct. If you want a summary, read the abstract. If you want rambling about where this fits in with other stuff, read the introduction. The conclusion may not be needed, but at its best, it's where the gold is. It's not about what you did, it's about why you did it and why other people should care. The rest of the paper is about closing off an open problem. The conclusion should be about what new things your contribution opens up.
The exhortation against new information is still accurate, it's just that it's more nuanced than that. Don't put in new information that's relevant to the problem you're addressing and the solution you've come up with. But do put in new information about things not addressed in the rest of the paper. There's prior work, which should be referenced in the introduction. There's your work, which is described in the body of the paper. There's future work, which is for the conclusion. There's also the layer above, the wider meaning and ramifications of your work; that's also for the conclusion. "What useful insight can I provide as a result of burying my head in this problem for months or years?"