However, for the model to work it will take someone more informed or serious about the future of news in a civil society than Eyeo or Flattr have so far shown.
That might seem reasonable from a publisher's perspective, but to most end users of the internet adverts have become a plague, blocking up bandwidth, conveying malware, and popping up/flashing/auto-playing video at every opportunity. From that point of view Eyeo (by blocking most intrusive adverts) is still doing a good job.
The supermarket analogy is very good, every major media producer has tried (and mostly failed) to control sales of their goods by legal threats and DRM. And it not really working, while the Pirate Bay may be fading from prominence, most artists are still not getting much from the "legal" replacements such as Spotify or YouTube. And they are not much more than an advertisement vector in many cases.
Nobody really wants to pay for using the Internet, any yet they are - via advertisement or their personal information being whored around - but generally they don't know it. A workable micropayment system and some fair rules for its use (e.g. pay and get anonymity (beyond the pay provider knowing) and no adverts, or free and get infested/whored as usual) could go a long way to "draining the swap" as they say these days, offering artists some reward better than adverts but probably not as much as the big media barons are used to.
So if Eyeo or Flattr are not up to it, who is any better?