The answer is 'maybe'. One advantage restaurants and Chefs have is a built in audience. If you choose to write a book you can market it online or at your restaurant. You'll have the ability to connect more deeply with your patrons. It could be additional swag in your online store. It might also serve as a tool used to attract potential investors demonstrating that you have a marketable process and a sound business methodology. A book will capture your history at a point and time. It may set the stage for more stories and future books to come. Lastly, consider writing a book if you think it would be fun. There's great art in cook books and telling the stories of restaurants and the hospitality businesses. Don't write a book if you think it will be a big revenue producer because it likely will not be. A published book will document your history and enhance your brand.
If you choose to publish a book there's never been an easier time to get your message to market for relatively little cost. Gone are the days where someone with a message had to pitch to a publisher, hoping to get selected.
What are the advantages to being accepted by a publisher? There's a cred factor. Publishers endorse your work and also have a access and audience reach. Your book will be found a public library which is really great.
If you choose to self-publish there are many avenues to choose from. Your book can be carried on Amazon.com creating a broad reach. While you won't boast the prestige of being promoted by a traditional publisher, if there's money to be made, you will keep more of it.
Some self-publishing houses are quite generous to the authors and offer several services of traditional publishing houses. Independent Publisher's Group is one example, their business model contends they make money when you make money.
What should you budget in time and money for your book? I know it's frustrating to always say 'it depends' but if you're willing to do the heavy lifting yourself with copy, layout and photos a budget of less than $500 is fair. If you want to save time, by relying on pros to create a showpiece to record your history and use in promotions for years to come, $10,000 to $15,000 is a great place to start. For turnaround time estimate three months on the low end and be aware of scope creep by drafting a book that will take a year or longer to produce.
If you'd like to explore creating a book and can work within the ranges quoted above:
If being a book author is right for you, after you're holding the finished product in your hand or admiring it on the device of your choice, then the need to promote comes in. Use all the social media channels you are using today to advance the sales of your book.
Should you write a book? Don't ask me. I'm biased. I'm a writer and can't get enough of books, especially industry and culinary books. If it suits your brand and you think it would be fun, definitely take the time to capture your history and share it with the world.