It's a great sentiment, but money is just the intermediary to the real political capital, which is speech. In our capitalist society, the latter can be bought to a degree -- radio, newspaper, and television adds, movies, books, endorsements, flyers, lobbyists, think tanks, push pollers, etc. -- which is how money becomes a problem. But these things still all exist if you say "candidates can only use government provided funds." So what do you do if, say, the cable networks all lean one particular way? Do they just get to de facto choose who gets to president? What if one person sees it as worthwhile to purchase all of them?
For that matter, what do you do about the funding of third party political commentary in general? It's just as easy to buy an ad or promote a movie or event saying "Candidate X is a great guy" as it is to hand him the money so they can do it themselves. IMHO it's less accountable because you don't see the purchaser on the published list of donors, and if the message is dirty or incorrect a third party probably doesn't care while a candidate saying such things can lose significant backing and reputation.
Maybe you say, "No one in America is allowed to publicly say or do anything construed as supporting a candidate without giving equal time to the other candidate." Okay, what about financing which supports issues said candidate is backing, never mentioning him but clearly propping up his campaign platform? Are we going to ban all advocacy of any kind?
The nature of speech is to be too broad and adaptable to be regulated without inadvertently regulating it in its desired forms, and the point of the 1st amendment is that the benefits of its free exercise are too valuable to set aside. I tend to agree with that, personally -- I think we gain more from unrestricted speech than we lose from malevolent entities trying to use it to their advantage.
Thankfully, while it's easy to speculate better ones, the present system is actually not all that bad. Yes, it confers *some* advantage to be able to spend 60 million when your opponent spends only 30 million. But the return diminishes rapidly. It's a huge difference being able to convey your message to a voter vs. not being able to. But compared to that it's only a little bit better to convey the same message twice, etc. In general, it's possible for candidates to get their say in even in demographics where the other candidate enjoys home turf advantage. And as much as we like to bemoan the "uninformed voter," the overall effect is to inform voters. The system is definitely inequitable, but not horribly so compared to other systems, and I think with little susceptibility to extensive influence by individual players.