> The diversity of screen sizes and browsers and DPIs is greater than it has ever been, and will only increase.

That may be true, but beyond a certain point, it doesn't matter.

In terms of physical size, it makes sense to have a single-column layout for small devices, where layout techniques like using multiple columns are never going to be very useful no matter how high the resolution gets. You might prioritise some content more highly and reduce or eliminate less valuable material to go with this. It also makes sense to allow for layouts that do have wider areas and/or multiple columns if the content can benefit and the display medium can support it. I doubt anyone is going to want to render most web pages with dozens of columns any time soon, though, no matter what physical size a screen might reach. Most content isn't going to benefit from that, because the human eye and brain can only take in so much at once anyway. So the big question here is how many discrete layouts are useful in practice, with a whole load of secondary questions about the balance between showing more content at once vs. allowing user interaction to navigate content in different ways.

In terms of resolution, the consideration is different, but there is still a general case. At low resolutions, it is worth having specific, pixel-perfect designs. At somewhat higher resolutions, it is worth having different pixel-perfect designs, to give sharper results at a similar physical size. Sometimes it is best if pixel-based designs don't try to copy all the detail of the "true" designs as they get smaller, but present simpler, cleaner versions of the same basic idea instead. At some point, your resolution gets high enough that scaling vectors representing the "true" designs by default and using techniques like antialiasing and font hinting becomes a viable alternative. Somewhere beyond that, vectors alone would be sufficient, as the eye isn't powerful enough to see any more detail anyway. The big questions are where on this scale you change from one pixel-perfect format to another, and how many such formats you produce before you switch to using scalable vectors.

In the real world, of course, these two ideas interact at times, and there is a cost/benefit trade-off as well. Perhaps you would prefer to have three sizes of pixel-perfect versions of all your custom graphics plus a vector, but in reality you might have only one or two and accept that content will appear at significantly different physical sizes on different devices. Perhaps you would like to have a responsive design with four different layouts, but in reality a mobile-friendly version and a regular site will do. You'll still be able to cater well to many different devices with only a small number of combinations if they are well thought-out, though.