I am aware of the fact that layout and function of a site should be strictly separated. Layout should be done with CSS and functions of the site, like expand mobile menu on click, should be done with JS.
Reference:1. & 2.
What I often see happening for responsive layouts is having column classes for the various media queries, where just the class name is different, however the width values are identical.
This then leads to HTML in the form of
<div class="container small-query-columns-4 medium-query-columns-6 large-query-columns-12><p>Responsive paragraph..</p></div>.
That's not bad idea but I think that it is not good idea too. I had thought about something similar few weeks ago. I wanted to make CSS which will be compiled in browser via JS in few loops and then appended to head section. But after deep thinking I decided to not doing that.
I know that you can make fallbacks and some fancy stuff so it works in every browser with or without js, but I have looked at my grid. It takes less than 10KB. It's interesting idea, but it isn't worh so much work as it will take. Keep your HTML organised and you won't run into issue with too many css classes. You have to let someone who use your "framework" do define widths at certain breakpoints. Easiest thing to do is just write a class name.
Consider that when you use for example bootstrap and want to have 12 columns on mobile, you just don't define it and it automatically falls into that width. Many times it just enough to define max 2 breakpoints with css classes.
When I think about enquirejs I think that it can be used for hiding sliders on mobile for example. When you just display: none it still running and changing classes. If you have something similiar what should be removed because mobile is not good environment for running something, you can disable it by using enquire. Another example is mansory grid, which you can start and disable via enquirejs.
Basically you can use it if you have something already js-depended and want to customize it on diffrent screens, or give diffrent behavior, because if you just set something on window load or document load, you have an issue with someone who resizes window. Here you can use it.