Right now Illustrator offers Retype function, still in Beta, which allows you to recognize and rebuild a text, if the font is installed on your drive or exist in Adobe Fonts. Have you tried it? It works on word basis, restoring one at a time.
This function was designed to solves tasks like you describe.

Another option you can use, a more honest one, is 'Create outlined text paths to editable text' button command from VectorFirstAid plugin from Astute Graphics. It works by comparing a chosen font with outlines and restoring positions precisely, for the whole selection (but requires unchanged outlines).

If you just need to save the font name when a text is outlined, I think it’s something that can be handled with a script... But it won’t be as different as the habit you already have, and won’t apply to the majority of users who don’t use the script.

Egor,

I think you'd be surprised how many designers convert fonts to outlines then need to go back and edit or add something but can't remember which of the thousands of fonts they used. Over the years, I've just gotten in to the habit of copying and pasting the text box and putting it outside the artboard to refer back to if needed.

I've worked on a couple of larger teams of designers, and there are plenty out there who do not have the best workflow methods. For example, ten designers could edit the same file over several years as needed, and there's no way to find out easily once that designer has moved on to another job. Or if you have to work on a PDF because someone accidentally saved the AI file as a PDF without the "Preserve Illustrator Editing Capabilities" option checked, and the AI file has mysteriously vanished from the shared servers. Opening the pdf back up in AI and being able to know what the outlined fonts were could be a huge help.

Interesting. For now you can do it manually by adding the name of it to the note field in the info panel. And it looks like a thing that a custom script can do. But I doubt that this can be a wide-needed feature .