Options for overwriting when rendering

Yeah but it's not the same I think, because if you uncheck overwrite and render your animation (without noticing) it won't actually output the render and again without noticing it won't be saved. Lol I think what OP meant is to automatically create a new index like render.002 render.003 which would be a fine idea

That'd be called "incrementing".

Personally, I'd love to be able to use global variables in names . That would allow many things, including having file names with increments, but also time stamps, scene data, system data, ... Many softwares do this, and even have a nice UI to help the user discover which variables are available and give a preview.

I like how ShareX does it. Just right click the input field and you get all possible variables in categories and human-readable labels:

Blender already uses # for frame numbers, it could be extended to way more. And we could even think of a python wildcard like %py() that can contain a simple expression or data path so that an advanced user can make its own variables even if not covered by the provided ones. I.E. %py(bpy.context.preferences.addons['someAddon'].bl_info['version']) .

yeah the Global Varibles sound amazing

automating naming conventions would be a huge time saver for repetitive tasks ( not to mention, that's where a lot of accidents happen when you accidentally overwrite something )

Disabling "Overwrite" in the Output panel is useful for image sequences, but there's no similar option when rendering videos. This would be extremely useful when the output path for a video is set to a specific filename.

There's an addon for that. Look for Blender Path Maker. It allows you to use expressions and python scripts to dynamically name your output files.