Funding campaings from public money is widespread in Europe. Sometimes the opposite argument is made: public funding ensures a level field, in which no one has a disproportionate advantage. Of course, this has the effect of displacing the battle to the real battlefields, one of them being propaganda, as you said.
Democrats and Republicans already control ballot access laws, a clear conflict of interest. Let us wave our magic wands and — poof! — campaign expenditures are now tax-funded. Nothing meaningful changes. The Republicrats still control who has access to the ballot and thus who will receive campaign largess.
“Public campaign finance” is no magic fix, rather it is welfare for already wealthy political parties.
If campaign financing will be restricted to public money, they won't be wealthy anymore and they will not be able to use to their political benefit any unrestricted hidden wealth in the form of super PACs. And this will also open way for the smaller parties and independent candidates to the fair competition.
If politicians are denied chance to get silently wealthy on their positions, we will have different kind of politicians: not relatively benign fat cats who are after nothing but money, but ideologically explosive 'great leaders' who want to change the world in the name of their 'great' ideas (there won't be much reason to go into politics otherwise, if you can't make much cash there). Do you really want any of them?
Corruptioners are the best kinds of politicians you may have.
Well, I already have plenty of politicians representing me as a result of recent elections, and they belong to neither of the kind, as far as I know. Here in Germany we probably have few fat cats, but the 'great leaders' are political marginals. The politics are done by parties, which leadership periodically changes, and the government isn't run by a single person able to impose their will on other ministers.
And people whose only jobs as adults have been elected or appointed positions will still mysteriously become worth 7 or 8 or 9 figures by the end of their careers, even though their only reported income has been a government salary.