DVI is still the primary output format for anyone using pstricks, an extended DVI format is the only output format from xetex as well as being the default (if not most common) output from pdftex, so I think the question in the title is based on a false premise.
What is true is that PDF has pretty much replaced DVI as a distribution format on the web (or before the web, on ftp and email). I think the main issue there is just the ubiquity of a viewer. If you use PDF output, or convert your DVI to PDF just about anyone with any sort of computer will already have a PDF viewer available. If you send someone a DVI file then if they are not already a TeX user they probably can neither read the file nor easily install a DVI viewer without installing an entire TeX distribution.