The reason there is so much conflicting advice going around about book publishing and book proposals is that in this area there are no clear rules, only different approaches, each with their own pros and cons, risks and rewards. Some authors do it one way, others do it another way; some publishers will only consider a largely complete manuscript, others are fine with a short proposal and a chapter or other sample. How you would want to go about it would depend on virtually everything about you, your goals and career situation, your book idea, and the publisher you are thinking of publishing with.
Here are some of the pros of submitting a book proposal at an early stage in your project:
- You will be able to get feedback on your writing and on your idea at an early stage. Especially if you are uncertain about whether your writing is good enough or whether your idea is attractive enough, such feedback can be crucial and enable you to either back out of the idea at an early stage without a high sunk cost if it turns out to be a really bad one, or recalibrate and redefine the scope of the project if the idea is good but can be improved even more using the feedback you get. The end result can be a much better book than you would write by yourself without any feedback.
- If your proposal is accepted, you will then sign a contract, which is a psychological reward that can motivate you to keep working.
- The contract will come with a deadline for delivery of the completed manuscript. Again, psychologically this is very helpful for many authors who may find it hard to make consistent progress with a project that spans several years without concrete goals, someone they are officially accountable to, and a timeline they can reference to measure their progress.
- Although (as far as I know) a book contract for a book in progress usually does not count officially towards tenure and promotion decisions, in many places it can count unofficially, in the sense that you can tell your colleagues about it, they will be impressed, and will be inclined to weigh your case a bit more favorably and to cut you a bit more slack for the reduced number of ordinary papers you will likely be publishing during the book writing period.
Here are some of the cons of submitting a book proposal at an early stage, or equivalently, the pros of waiting until your project is more mature:
- If your writing and the book idea are good already without any feedback (or if you have some other very knowledgeable person who can give you feedback so you don't need the publisher's input for that), then your proposal will have a higher chance of being accepted if you submit a more mature proposal later on when you already have several chapters completed, since the publisher will see that you are serious, committed to your project, and will have more completed material by which to judge the proposal. (In an extreme case, when you have a finished manuscript, obviously that can be quite reassuring to a publisher and eliminate a large source of risk to them, again assuming the book is actually good.)
- This one is a bit speculative, but I believe that for similar reasons, submitting a proposal in a more mature stage of the project puts you in a better negotiating position. As a result, you might for example aim to publish with a more prestigious publisher than you would otherwise. Or, depending on how much you care about the terms of your contract and what precisely you are hoping to achieve, you may be able to negotiate higher royalties, or other things about the book that may be important to you (e.g.: color figures; keeping ownership of the copyright, translation rights, rights to use another publisher for a future edition; permission to make the book available to download on your personal web page; etc.). Money-wise you almost certainly won't be making much money anyway so it's probably a non-issue, but the other things could be important and are worth putting some thought into.
To summarize, this decision is a delicate balancing act. Much depends on factors like where you are in your career; your personality; how many years you can afford to wait before you get the satisfaction and professional prestige of a signed book contract; how much you trust yourself to deliver on a very substantial commitment made early on in the life of the project when you are still full of passion and energy (trust me, by the time it's over you'll want to never look at the damn thing again...); how confident you are in the quality of your work; how much you value and need feedback from others; and many other things. Good luck!
[Source: personal opinion, informed by my own experience publishing a book.]