Advantages of installing a program with Homebrew-Cask? With Homebrew-Cask you can install many programs such as Google Chrome or OmniFocus. I can come up with a few advantages:


You can install programs without going though the process of finding the download link, possible mounting the image, and installing it if contains an installer (although this doesn't save too much time unless you're trying to reinstall many programs on another computer)
You can uninstall the programs fairly easily


Looking at the website, they list three advantages: 


Install with ease – this I mentioned above
Unix-savvy, macOS-friendly – here it mentions applications are installed in /Applications or any other configured area, which is nice but not a game-changer
Community-driven – this is mainly useful for enthusiasts or for people who want to make their applications compatible with Homebrew-Cask


Other than the two reasons I could come up with, I don't see any other huge advantages. Are there any that I am not aware of? While uninstalling programs using brew cask uninstall, do all the files associated with the app get removed, à la AppCleaner? Is it comparable to AppCleaner?
Two other main points are that it makes a) updating and b) transfering your setup to another machine extremely easy.

The uninstall capabilities depend on the "quality" of the cask for the program you uninstall. There is no "general" complete cleanup afaik.