Well, even politicians have a common interest in winning wars, as do all citizens. As for winning elections, there are a myriad of fiercely competing interests. Because some in the public understand this dynamic, politicians will no doubt argue that money would have to be even more tightly controlled. Some bureau, or agency, or both (or a dozen) would have to set up finding for each election, and the only money that could be spent on that election would be the money disbursed by the government with regulations predetermined by incumbent politicians.
And here's an even simpler system: If you really want to take money out of politics, just stop holding elections. Period. If there were no elections, there'd be no money in politics, other than the paying of representatives. Each current representative could appoint his or her successor, and you could regulate the politicians' financial concerns all you (or they) like . . . and that way money would no longer be a problem.
You see, the easiest way to take money out of politics is to take democracy out of politics.
In a democracy, people need ways to influence other people, and spending money advertising each case is one of those ways. It's integral. If "money and politics" were your only concern, then taking the democracy out of the representational system would work just dandy.
And after all, it's not as if the regulatory/redistributionist state (the "welfare state") requires democracy. It's a very old idea. You could say it was invented, in ancient times, by the Roman Empire, with its bread and circuses. A socialized retirement system was invented, in modern times, by Otto von Bismarck. It's easier to direct without hordes of interests "having a lawful say."
So, if you really want "money out of politics," you have two choices: Take politics out of money, by limiting government power to meddle in every aspect of society; or take democracy out of government.
Do you detect a reductio ad absurdum? Maybe. But this solution is merely a more honest option than the politicians' preferred plan.
After all, socialized elections are undemocratic, too, undemocratic in a very practical sense. They would be so regulated as to channel dissent. It would be even harder for upstarts and challengers truly to challenge incumbents. Every step since Watergate to regulate elections has increased the power of incumbency. We have a startlingly high incumbency success rate now. That would likely increase in socialized elections. Socialized elections amount to a mere halfway measure to getting democracy out of politics.
Which is perhaps why the "old timers" in politics are now coming out for it. It would so play into their hands.
It would lead to democracy precisely as they like it: democracy without citizen control, democracy in name only.