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.
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/...
There is another way to look at this problem though by asking why there is so much money being directed towards elections and politicians? One cause is the increased size and scope of government. When the role of government expands into more aspects of our lives via various regulations, subsidies, penalties, and so on it creates an incentive to influence the creation of those regulations, subsidies, and penalties.
A smaller role for government, in particular a reduction in policies that try to pick winners and losers explicitly (e.g. taxes or fees that favor particular companies or industries), could reduce the incentive to influence the creation of "targeted" legislation.
Another approach that doesn't conflict with freedom of speech goals would be better transparency about the source of monies through more aggressive disclosure rules.
Exactly. Companies look at the dollars they spend and ask themselves, how can I get the best return on spending this dollar? As government regulations increasingly influence their bottom line, companies will increasingly conclude that spending money influencing regulations is a good use of their money. Hence, more lobbying.
Redistricting won't save democracy; at best, algorithmic or "mathematical" (a fool's term for neutral and objective) redistricting will allow for the voters to pick candidates that are proportionally and geographically anchored to their districts. Geographical picking of representatives isn't broken beyond repair within the political system, nor is the physical counting of votes to determine which representatives win, though the electronic voting systems leave the latter terrifyingly unverifiable and unquestionably anti-democratic.
The slaughter of democracy in our time is an intentionally engineered result of post-election corruption as effected by bribes of lobbyists, raping the power of the vote in the name of capital flow to those that are already morbidly obese with riches. You cannot have democracy when money is allowed to have a coercive power that eclipses any feasible democratic comeuppance.
Let the banishment of money from the election component of political activity exist as an iron law in any new democracy which is established. That would be the start of having a fighting chance for democracy, which America has long since discarded.