Sites today should be designed to accommodate a range of display/window sizes. This depends upon the content, but, ideally would work on displays from 240px wide to 1920px (or so). For some content this is not practicable, e.g. complex tabular data may not be effectively viewed on a smartphone.
Having said that, I dislike seeing the text shuffling about as a window's width is altered. So I'm working on what I call a "snap responsive" layout that:
For devices with a screen width of 480px or smaller display full screen.
For devices with a screen width exceeding 480px, a range of widths can be supported, with the page "snapping" from one to the next.
I originally thought that a step size of 80px would be optimal, but, testing this assumption has led me to increase the step sizes to 160px.
Some people may regard this as a retrograde step: an attempt to persist with using fixed width design techniques in a responsive context. It is true that each step behaves like a fixed width design, but the reasons for the design are quite different. And a step-responsive design is no simpler to code than a responsive design, indeed they are very similar.