So long as the state appropriates and controls a vast share of resources all the people will vie for a share of it. They will find innumerable innovations. Those who have the means (money and influence) on their own always find a way in. So many of those of lesser means find ways to band to together to push themselves up to the trough. This leaky boat cannot be made seaworthy. [2]
"Public election funding" is another way to say, "Let's give the current incumbents monopoly control of the financing of elections." You can bet that whatever initial formulas they devise for distributing this cash (which confers the power to decide elections) while everyone is watching will be creatively "improved" soon after the public has shifted is gaze. Even when the initial formulas are evenhanded, we see unintended consequences. [3]
[1] http://www.opensecrets.org/orgs/list.php
[2] https://mises.org/library/politics-cannot-be-fixed
[3] https://www.washingtonpost.com/blogs/monkey-cage/wp/2015/01/...
I think this is incredibly short sighted. Money is a means to access a political voice for the dispossessed as much as the wealthy. What will happen without money is that policy will be crafted by and for solely the politically privileged. Backroom deals and dark access will be even more important than otherwise. A tighter, more difficult to disrupt oligarchy will emerge. I doubt this is what you would want.