I am just wondering if there is a hosting company which provides free SEO tools or other web site promotion services for its customers. I know the companies which provide their customers with free domains if they buy their hosting, but I have never heard of hosting companies which provide free website promotion services for their clients, do such companies exists?

most hosts actually have an option which allows their users to submit the site to certain number of search engines which is pretty much useless promotion method anyways. thats all the promotion they provide as far as i know of.

They do that for promotional goals. Web hosting company provide web hosting service and they might be not skilled in the SEO or SEO related services.