One, it is meant to be read alongside The Timeless Way of Building. It is not simply a how-to manual.
Two, it comes from experience gleaned in the field working as an architect and builder. It is not simply highbrow art, mysticism, or eccentricity.
Three, the patterns are separate from implementation: "[You] can use the solution a million times over, without ever doing it the same way twice." He goes on to distinguish patterns in which he believes an invariant property has been established from those in which more research is needed. He even states that some patterns are just a guess and shows how to identify those in the description of each pattern.
Lastly, he states there is a danger that people will assume that this one pattern language should stand for all time: "Is it not true that there is a danger that people might come to rely on this one printed language, instead of developing their own languages, in their own minds? The fact is, we have written this book as a first step in the society-wide process by which people will gradually become conscious of their own pattern languages, and work to improve them."
The purpose of the book and its principles is not to recreate an aesthetic through pastiche. You are meant to use the principles in the book to create your own language that works for your context. A pattern that works for me in my environment may not work for you. That fact doesn't nullify the value of the pattern. The purpose of the two books together is to acknowledge that humans have deep feelings about the environments they inhabit. Whether those feelings can be explained or not is beside the point. The point is that we have them. These feelings happen across cultures and time. When we apply those feelings about our environments to the built world, several patterns seem to emerge. Hence, you get the concept of pattern languages.
Alexander takes the bold step of not only acknowledging human feelings but centering them in the discussion about how the world should be built. This point should interest those who are sympathetic to the Agile Manifesto, or to principles of user-centered design, or to product design and product management. This fact is also likely why certain interests are uncomfortable with his work. Powerful interests do not, in general, like to lose power, and change is expensive.
Later works, including his series on The Nature of Order go deeper into his exploration of these principles, even the possibility of an objective evaluation of beauty. And yes, there is a bit of woo going on which can make some people feel uncomfortable. We are all capable thinkers. You can decide for yourself which ideas resonate and which do not.
Personally, I found that his ideas changed the way I experience the world, including giving me the ability to evaluate the kind of home I want to live in and how to optimize that home to increase my own happiness. I may not ever get the chance to build my own home. But I have a voice. I participate in society. I believe the world could and should do better than optimize itself for money. I believe I am not unique in finding the books useful.
(edited for clarity)
