I have a big folder on my computer of homeworks I've finished for various companies over the years. If I recall I passed all of them, it's sort of annoying that I can't simply hand over this list of other projects I've passed and say "here, all of these companies thought this was good".
What I like about your proposal is that if many other companies did it, the result would be every few years I should take a month of evenings and build out a cool project for myself demoing my ability to write code. If life gets to busy, it's fine if the project ages a bit.
This way you can scratch a personal itch and prep for interviews all the same time.