And that's where the donors come in, they fund the advertising and face time to get the signatures. Those without big money simply don't get the sigs. And, where is this money going to come from? You're talking about a lot of it when you're talking about national politics.
That's not going to happen. They have to be paid, or they won't do it.
The problem is, by the time they get to that level, we're already faced with the limited number of candidates the major parties have selected for us, just like we are today. It's a laudable idea, but we'll never get the money out of politics, it always follows the power.