Self-publishing academic book

I am an amateur mathematician. I am writing a research monograph in the field of abstract mathematics (general topology, specifically).

Should I publish it traditionally or self-publish?

There are many benefits of self-publishing (e.g with Lulu) an academic work:

1. No need to tremble awaiting my book to be rejected by a peer review. No responses like "first publish in articles, only then make a book". I am in full control what I want to publish.


2. I don't pay the publisher 80-90% of my revenue. (This also may make AdWords marketing of my book profitable and thus I can do a rather huge advertisement of my book myself using AdWords. I suspect, this may over-perform traditional publishers in the number of sales.)


3. I am in a full control of my book. No forced need to change something, if an editor's opinion differs from my own.


4. No need to convert it to LaTeX, I can use my preferred software such as TeXmacs.


5. The book goes into Amazon and other distribution channels anyway.

I can pay a professional scientific editor to edit my book for paid, as a kind of business investment.

Peer review is intended to choose which books are published and which are not. I can do fine without peer review, allowing the buyers of my book to decide for themselves.

Well, a potential buyer may prefer books published by a big publisher, but it (in my opinion) can be well replaced with big red letters "Edited and checked for errors by professor XXX."

Drawbacks which I know:

1. It may not be as good for my academic carrier as traditional academic publishing. (It does not matter for me anyway, as I am not a professional academic.)


2. Not sure if my book goes into university libraries (please comment on this issue).

I've pointed many benefits of self-publishing. What are drawbacks (except of pointed by me)?