I like how you put "you could theoretically build a car from scratch". As someone who writes about and uses React daily, and have written things from scratch before, that strikes me as a really good way of explaining the utility of frameworks to newcomers.
While most apps with any complexity will end up using some sort of framework, there is no rule which says it has to be an existing one. In my experience, a lot of the more involved projects I've worked on have used their own custom framework (as opposed to React, Angular, etc.) The upshot of this is that it is certainly possible to build something worth talking about without using one of the popular frameworks.