Package management is nowhere near 'only necessary if apps share dependencies'. Compare:
1) Search google for software. 2) Search software website for download link. 3) Download. 4) Go to folder it was downloaded to. 5) Run installer. 6) Click next five times.
The same situation, but with package management: 1) Type in a single command and watch it install exactly what you want, quickly. eg: `pacman -S firefox`