That is a thing that CSS allows. Flexbox, responsive design -- it's all optional. There is going to be a sense when you use CSS that way that you are swimming against the grain, and that's on purpose because it's important that the instinctive default way that new designers think about the web is in those responsive terms. But even if the web pushes you in that direction a bit, it's not a requirement -- you can still design interfaces the way you're talking about, and you can heavily use breakpoints and you can have different layouts depending on the situation.
One thing that I see websites do fairly often (which I don't think is great practice but I'm throwing it out as a common practice and I understand why people do it) is literally have two versions of their menus for mobile and desktop in the same interface in the same DOM tree and just throw a "display: none" on one of them depending on the width of the screen.
So it's not even necessarily that you have to serve different HTML, you can have different versions of components even on a completely static website with no JS that swap out seamlessly depending on the user's device size.
