ArtOfWarfare, how old are you? (not asking as an insult, it's a real question) The idea you're talking about sounds like something I might've thought of in my younger days.
This idea, while nice, will never happen because anyone willing to do it is already doing it. Any software developer who's willing to give away their software for free to anyone who needs it while also expecting people to pay for it if they can, they're already doing what you're talking about. It's called shareware or freeware (or more specifically, donationware). The idea behind these wares is exactly what you're talking about. If you need it but can't afford it, you're free to use it whenever you want, but if you can afford it then you are supposed to pay for it. If you need it but can't afford it you don't even need to wait for a special 'free software day.'
This idea, while nice, will never happen because anyone willing to do it is already doing it. Any software developer who's willing to give away their software for free to anyone who needs it while also expecting people to pay for it if they can, they're already doing what you're talking about. It's called shareware or freeware (or more specifically, donationware). The idea behind these wares is exactly what you're talking about. If you need it but can't afford it, you're free to use it whenever you want, but if you can afford it then you are supposed to pay for it. If you need it but can't afford it you don't even need to wait for a special 'free software day.'