Currently with designing and your dashboard to Tableau Server or Online you have the option to let the dashboard size automatically OR pick one, and only one, fixed screen resolution. I generally use the latter to be sure of how it will actually appear to the user, but the downside is that it tends to look rubbish on really large or really small (mobile). One way around this is to save and publish different versions of the dashboard, e.g. one for desktop use, one for mobile use, but I think this is sub-optimal.
My idea is that for one single dashboard you could set more than one screen size. In Tableau Desktop you could create and toggle between these, setting the layout for each independently. Only the layout would differ, the content would be the same. For example I might publish one dashboard with three different, fixed-size, layouts. One sized for a standard monitor, one for iPhone and one for printing out on A4 paper.
For the user, accessing the dashboard through their browser, Tableau Server / Online would serve up the size most appropriate to the machine they are accessing it from (retaining the cache-speed benefits). And if they print it - in my example above - it would automatically print the version with the (A4) layout designed for that purpose. The user would be completely unware that different versions even existed, to them it would be just one report, which renders nicely no-matter how they are accessing it.