Couple of things.
1) Automatic is bad because things break in unpredictable ways. Alignments get out of whack, any floating elements you may have don't scale up/down with the rest of the non-floating elements, and so on.
2) Keep in mind the distinction between SIZE and RESOLUTION. 1920 x 1080 is a resolution, not a size, so a dashboard built to those dimensions will look exactly the same on a 27" desktop monitor and a 55" conference room TV with Full HD resolution. If you're projecting to a different resolution (4K/UHD for instance) THEN things will look weird.
My usual problems are;
1) Projectors are often 4:3 (1280 x 1024) output rather than 16:9 output (1920 x 1080 or Full HD). That's more of an issue than raw resolution.
2) Large TV's being used as conference monitors don't have as much control over alternate resolutions as computer monitors. It's relatively easy to set a monitor to a resolution other than its native one (so you can make a 4K monitor into an HD monitor with little trouble). That CAN be harder on TVs (not always, maybe not even mostly, but it can happen).
So, depending on what problem you have, your options are different. You may be able to make use of Tableau's built-in ability to generate different dashboards for different screen sizes/shapes/resolutions - look for the "Device Preview" button when you're on a Dashboard page and try it out. That's the easiest solution, if it meets your needs.
Otherwise, you're stuck building different dashboards for different scenarios.
Michael makes some great points. I'll add that Tableau Server performance is the most common consideration. If the the people viewing a dashboard have a variety of different screen sizes or embedded iframe sizes, then this can cause Server to do a bunch of extra work (computing and relaying out each viz as well as the dashboard). It then has to cache and serve up all of these various dashboards. Defaulting to a fixed size dashboard makes this less of an issue. So, consider how the dashboard will be accessed by your viewers. Also, spend some time looking for ways to performance optimize the design of your dashboards. I like this article: 6 Tips to Increase Dashboard Performance.
Product Manager, Dashboard Apps Dev Team