In addition to all the good arguments in https://tex.stackexchange.com/a/301974/36296, and leaving the
TeX level, running your code with a local distribution has the advantage that you can use whatever editor you want. Some offer pretty convenient features, just a few examples from the top of my head:
Shortcuts and even custom shortcuts: Often using the same worklflow? Assigning it to a shortcut can save a lot of time.
An editor you already use: Use one program you already know from other tasks like programming.
Code snippets: Use the same code building blocks again and again? Code snippets can make it easier to find them.
Buttons/menus/displays etc.: Many editors provide plenty of features to help writing tex code. Menus to select font sizes, hierarchical structures like
sections, various kinds of letters and symbols - Graphical assistants to insert figures or edit tables - autocomplete commands, words or labels and cites - display tooltips about commands ...
Of course they are not available in every editor, but remember, working locally you have the freedom to choose whatever you want. For a list of available editors, including their main features, see, e.g., LaTeX Editors/IDEs
Besides these considerations about the editor, on your own system you can use all the cool Tools for automating document compilation whereas overleaf only uses
latexmk (as far as I know).