I agree that an addon should not be necessary, for production this is a basic need and great to find its way into Blender core by a developer that can find some time for it.
What Do you think about the idea to set a checkbox “save incremental” in the Preferences, so the shortcut Ctrl S would save incremental automatically.
Blender does something of “incrementaling-ish” (by creating this .blend1 and .blend2, … files), so if instead incremental save (like myProject - 0001, myProject - 0002, …) would be activated by default, but could be turned of for people who like it organized the old way (.blend1, …) they could fall back on that while others would have a more familiar organization of increments.
My toughs are, giving an extra “Save incremental” option in the “File” menu just to save incremental is maybe a bit much, because:
turning it into the preferred mode once is enough for most people
Especially new users don’t know what incremental save means often and may get confused unnecessarily if the option could be turned on by default or can be checked at will anyway.
Your Mock up somehow got me thinking, what if the following options for incremental save would exist, that writes out the date and time in front or at the end of the filename like:
myProject 2021_07_20 - 11-20-59.blend
2021_07_20 - 11-20-59 myProject .blend
The second way could be helpful if at different design stages the Project name changes, everything would automatically be sorted chronologically. like:
2021_07_19 - 15-13-52 myProject - whiteboxing Ralf.blend
2021_07_19 - 15-14-34 myProject - whiteboxing Ralf.blend
2021_07_19 - 15-14-49 myProject - whiteboxing Ralf.blend
2021_07_20 - 11-20-59 myProject - feedback Stanley Kubrick.blend
2021_07_20 - 12-14-11 myProject - whiteboxing Ralf 2.blend
This would make it easy to jump back to a stage the design or animation was better, because often we remember the time the animation was good, like
“oh yesterday afternoon I had something on the right track, but than I started to overthink after Stanleys feedback, and messt it up, let me jump back and start over from that point”