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.

Makes sense to me! Probably not worth re-installing programs I already have, though, would you agree?

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.