The /applications folder is for .app bundles; Homebrew mostly installs Unix binaries which are appropriately placed in /usr/local , just like many Apple-supplied binaries are in /usr. The two conventions work well side-by-side.
The vast majority of Homebrew packages are not available as .dmg or .pkg ; installing that way also is a huge PITA when dealing with a myriad of small developer tools that require dependencies, whereas brew manages all of that for you, including upgrades.
The vast majority of Homebrew packages are not available as .dmg or .pkg ; installing that way also is a huge PITA when dealing with a myriad of small developer tools that require dependencies, whereas brew manages all of that for you, including upgrades.