Actually, many primary campaigns were funded by public money. There was an interesting episode of Planet Money recently [0] where they talked to Senator Fred Harris who got the US system started. A few years after getting it going, he used public funds to run against Jimmy Carter for the 1976 nomination by the Democrats. He lost to Carter and then Carter used public funds to run his presidential campaign against Ford. But Harris got ~$600,000.00 to run his nomination campaign.
It's really surprising how often something trends on HN and there's a relevant Planet Money episode from within the last few weeks. I wonder if that's because in some cases other news outlets are spurred into covering it because of Planet Money (it's reach is relatively small compared to the Guardian, so the Guardian covering the topic will be seen as new to most), or if there's some journalistic social network (in the traditional sense, not the Facebook sense) that some outlets are better are responding to quickly than others?
[0] http://www.npr.org/sections/money/2016/03/25/471905383/episo...