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There is no need, but it is just more practical to install software using Homebrew, given that it is highly scriptable, it harmonizes the installation processes of different software packages and its formulas are regularly updated. It also often offers more options than a regular installer (bindings, compile options, etc...). I agree that Mysql's binary distribution is totally fine, but there is nothing wrong with installing it through Homebrew if we don't need all the bells and whistles coming with Oracle's installer package.
Have a look at oh-my-zsh's plugin page. Git is only one of the plugins that comes by default. There are many others that are useful for almost any task. Now that your a Z-shell user, make the most out of it! ;)