Mair's argument is that it is a waste of effort to spend time on learning the characters, in the first stages of learning the language. They are more easily learnt systematically somewhat later on, when you know the corresponding words to which you can anchor them. Note that the people advocating for this are university language professors and teachers, who are claiming they have data backing up the claim.
As an adult student of the language, my experience is that I was glad to start without the crutch of romaji, for a simple practical reason - Japanese quickly becomes tedious to read Romanized. Kanji + kana are much more compact, and things like the conjugation of a verb and doubled letters which are common in the language are immediately obvious - because the writing system is designed to accommodate them.
Learning 2500 kanji from the beginning is a major cognitive task that shouldn't be a primary focus, nor is it in native Japanese language pedagogy. But learning the kana is simple, again I learned them as an adult and had them down cold in a few weeks of active classwork. My kanji retention is terrible, but learning materials almost always give the reading of kanji using furigana, and there are useful tools for annotating web pages, etc. with furi readings.
> Kanji + kana are much more compact, and things like the conjugation of a verb and doubled letters which are common in the language are immediately obvious - because the writing system is designed to accommodate them.
My grasp of Japanese is virtually non-existent, but I noticed this as well. Taking an example from the post, I find something like しっけ easier to parse than the romaji shikke. The latter form just feels clumsy for reasons I can't really articulate.
It also makes the pronunciation a little easier at times. If I read "desu", I read it with a fairly pronounced "u" sound. Reading です, on the other hand, I know without really thinking about it that the う sound is typically very short.
I think it's because most hiragana/katakana is in the form "consonant-vowel" meaning that almost all words are made up of collections of 2 letter sounds/syllables. This gives words a certain cadence which is easily repeated. When you convert that to romaji you begin to parse the words as though they were english and the discrete "consonant-vowel" sounds get broken down and become harder to see/read.
Really though, you can learn hiragana in a single sitting using mnemonic trickery and you can commit it to memory using a spaced repetition or flashcard system in a few days. Not learning hiragana and katakana seems much more of a hindrance than "wasting time" by learning it.
Right, my counter to that is that's great if you want to leisurely learn Japanese, but also not very relevant for the type of course this book supports. These typically start you on kanji pretty much in week 3, in conjunction with the word lists that support the kanji you're learning every week (and constantly use throughout that week and subsequent ones), specifically because of the argument raised: learning kanji without the words they're in, and even if that, without using those words, is ridiculous.
The argument above applies specifically to university courses, and was made by someone who is familiar with teaching such courses. So I don't think you can just discount it with handwaving, especially as there are claims about better success rates.
I'm not discounting anything, but different people want, or need, different courses.
My book is geared specifically towards people who are to enthusiastically committed to learning Japanese, and want more information about the language they're paying money for to learn, with some assumptions about what that means: they, like me, and like many of my fellow students at the time, but not like everyone, want to learn Japanese properly, without hand holding because some grammar or some orthography is deemed too hard. We'll see whether that's the case as we learn, not as an assumption baked into the course.
Of course that method doesn't work for everyone, but for me, and for many others, but again not for everyone, getting kanji early was exciting, motivating, and awesome. I would have been angry at a promise of a better approach without kanji for half a year as a paying student.
So that's the book you get here, too: I am not making assumptions on how slowly you want material, this is a grammar for supplementing your course work, or deep diving if that's what you want to do. And if the Japanese used in the book is too much, too soon: it's a free book, find one you feel fits you better. But we're better off with a spectrum of works: rather than every book following the best methodology, we need all those methodologies, and then people who go hard, fast, can pick the hard, fast books, and people who don't can pick the slower, "better success rate" approaches and do well with those instead.