Same reason people love package managers in general. A single bash script can install all the programs you want. Add Homebrew Cask and even your GUI apps can be included in that script alongside wget, vnstat, whatever.
Yea, I only do a "brew cask search" for new apps I want to install. I believe you would want to avoid attempting to re-install an app via Cask that was installed normally (~/Applications vs /Applications). Personally, I would do a clean install to transition an app to being managed by Cask.
