I don't think just giving the money to whoever has a prototype is a good idea. Some culturally relevant projects aren't the sort of thing you can make a prototype of, but I like where you're going. I'd amend it like so:
Once I've been a citizen long enough (i.e. paid enough taxes) I get to invoke my free year, which is a year where the government pays me enough to cover my bills and maybe a bit extra for projects and stuff.
During this year, I am encouraged to make some kind of contribution: maybe I start a business, maybe I do an art project, maybe I try to overthrow the government, it's up to me.
At the end of the year, I can provide a presentation about what society gained by funding my free year. If I do, it goes into an archive and part of the voting process means having citizens review these and decide whether I deserve another free year to persue similar endeavors. Maybe voted on free years are actually two years long so you can be more ambitious once proven viable.
So if society likes what you do when left to your own devices, they have the opportunity to keep funding it. If not, well you had your shot and nothing stops you from carrying on the old fashioned way.
As for yourself, you get to decide when to invoke your free year. Is the idea really ready? Do you have the skills? Should you put a bit more work into it on the weekends before you try to do it full time? These things ought to ensure sufficient seriousness from the participant. You can have a video game year on the government's dime, but unless people really want their tax money funding your gaming, your only going to get one.