A rich set of comments. Several suggest that the solution to the "soft bribery" problem is to require that all campaign contributions be anonymous; then no one could prove that he had contributed to a particular candidate. The problem is that, since "soft bribery" is an important motive for contributions, the total amount of contributions, and hence of political advertising, will fall, and so there will be reduced dissemination of political information. That is a loss. I do not know whether it would exceed the gain from reducing the amount of soft bribery, but it might well. The brunt would be borne by new entrants, who need to advertise more in order to make a dent in the "brand recognition" of incumbents. In addition, the wealthy, who are the big donors, are not a monolith; they have competing interests and therefore provide virtual representation for many ordinary people, such as the employees of the big corporations. Also the wealthy do not have the votes; their political advertisements are aimed at average people. Furthermore, if some candidates court the wealthy, this will drive others to raise money from the nonwealthy, something that the Internet has made easier to do, as we learned in the 2004 presidential election. The nonwealthy give less per capita, of course, but there are vastly more of them.
Still another point is that even the wealthy do not care solely about policies likely to benefit them. They also care about leadership, always a major focus in a presidential election.
I agree with the comment which suggests that increased political advertising could reduce turnout. The politicians are not interested in maximizing turnout, but in winning, and a winning strategy may be to depress turnout if higher turnout would produce more votes for your opponent. Negative advertising might provoke counter advertising also negative, the net effect of which was to reduce turnout but to the advantage of the candidate who had initiated the negative campaign.
I do not agree, however, that advertising in commercial markets is likely to depress output (the analog of turnout in the electoral market). The comment that argues this points out that in a cartelized market, that is, in a market in which the sellers have agreed not to compete in price, there is a tendency for nonprice competition, including advertising, to increase, as sellers vie to engross the largest possible share of the profits generated by the cartel price. I don't see how forbidding advertising in such a setting would result in higher output; it would simply increase the sellers' profits at the cartel price. On the contrary, by reducing the erosion of cartel profits through nonprice competition, the advertising ban would tend to make the cartel last longer. But in any event there is no price competition in the political market because politicians can't buy votes directly. Advertising (broadly defined) is the only permitted method of competition.
Finally, I disagree with the suggestion, common though it is, that unlimited campaign spending impairs democracy by giving political power to the wealthy, or more precisely to any individuals or groups able and willing to spend disproportionately to support particular candidates or policies. The suggestion confuses democracy with equality. Democracy is the political system in which the principal officials are forced to stand for election at short intervals. The identity and policies of the officials may well be influenced by the underlying distribution of income and wealth in society, but that does not make the society less democratic.