Seems like it would solve some of the stated problems without arguing over what some would call a "loophole" but others would recognize as "free speech."
Then the game changes to who gets allocated said public money. Can't see how that wouldn't entrench the establishment a zillion times more. Note Trump's effectiveness because he can ignore the Republican Party donor class riot, which is in stark opposition to the majority of the party's base.
For those eeeevil people who nonetheless managed to get some, prosecuting them for not following one of the zillions of non-statutory but still the force of law rules they will inevitably break. Using another example of fighting gun control (because I know the most about how this has played out since the early '70s), here's just one notorious example of how that "works" http://jpfo.org/filegen-a-m/cac-info.htm (note, that's from a very partisan group, not the milquetoast NRA). That's sort of thing is also happening in Connecticut right now post-Sandy Hook.
Ah, and a useful analogy from fighting gun control: a lot of the laws in place and proposed are, as Michael Bane put it, "flypaper laws", designed to trap the unwary in "crimes" entirely lacking in mens rea or any actual good public policy results, resulting in a chilling effect on Constitutionally protected actions.
Same exact thing here, "campaign reforms" by the goo-goos, especially financial ones, have a greater chilling effect on genuine citizen grassroots actions. You have to hire really good legal council, and surprise, surprise, pretty much all those lawyers are already retained by the existing political parties and their units. And even then we see atrocities like the political prosecutions of Tom Delay and Ted Stevens, eventually reversed by higher courts but not before accomplishing the mission of removing them from politics.
In theory there could be a large tax on broadcasting/advertising with the proceeds going equally to every declared candidate who can meet some threshold number of constituent signatures. Then the more money people spend on political advertising, the more each politician gets to respond to it, but the entire scheme is content-neutral.
Would the government give out money to anyone who ran? How do you stop someone from using the funds for an election campaign that is indistinguishable from an audition for FoxNews or MSNBC contributor? No matter what the bar is for funding, the government would be picking winners and losers, right?
Would you ban private donations to campaigns? What about private speech that advocates for a candidate?
I'm not sure what that public money buys us that other regulations couldn't do better.
If we're worried about getting information to voters, requiring all public debates be in the public domain and posted in standard web formats seems like a sensible first step.