Since you cannot legally tell a person how much of their own money they can spend on campaigning (numerous SCOTUS cases) and you cannot distribute public money without having set criterion for doing so (determined by an unelected clerk).

Campaign finance laws are merely incumbent and/rich candidate protection laws.   

And no that money won't leave 'politics' or the power sphere related to policy.  Instead it will shift to influencing said unelected Clerk to allow or disallow money for certain candidates.   It will also dramatically increase the number of candidates to get free money.....  cause anyone can run for office and get free (public) campaign money