No, it isn’t necessary to build a blog page in website for SEO. But if you build a blog page on a website it can help you to rank on multiple keywords and provide information to users.
The main purpose of a blog is to provide valueable infomration to users but if you are not building it then there are many opportunities that you will lack if you want organic traffic.
There’s another aspect of this is that when you are building a tool website then you don’t need a blog for it because users are coming to your website for performing an action rather than reading stuff.
So, it all depends which kind of website you are building if you are building a informational website then you should build a blog but if you are building a utility or tool type of website then there’s no need of it.