1) Something of a red herring, my VOIP provider starts sending me emails when by balance drops below $20. But it works well in terms of periodically topping up the balance.
2) For markets to work it is essential for them to reward individually. A basic income for authors would simply raise the noise level, an income for "quality" authors based on readership encourages an increase in signal level.
3) Perhaps we could use the phone call method, and accrue fractions of a penny the longer you stay on a page. I agree that you would want to be able to express a desire for less click baity and more useful articles, the mechanism for that isn't as clear.
On the whole piracy thing, I presume you were around when NetFlix streaming knocked the winds out of torrent streaming? It didn't do it because it disable the torrent protocol, it did it because people who had been pirating content switched to Netflix because it was a better service experience at a price they were willing to pay. That is a very very important lesson for content providers. Their pricing authority is extremely limited in a high tech world.
I like your story but we both know that the guy next to you would quickly be out of free $10 bills, and then he would have to go to the bank and give them some money for another stack to give away, and eventually, like content providers today, would get tired of giving away $10 bills to people. And eventually he would run out of the funds as well.
The basic economics of a functioning market are that suppliers try to get as much as they can for their product and buyers try to pay as little as they can. The process for creating the process creates a price floor, below which nobody makes the product because they go broke doing so. Between that sad place, and people paying way more for a product than it costs to produce, lives the market economy.
Historically people have argued that information flies in the face of this view of the world, after all if I can produce infinite supply of something (copies) shouldn't the price go to zero? And yet it doesn't. I've spend about 20 years looking at how information gains and loses value, and how people can capture that value in a transaction. Google, for example. doesn't sell the eyeballs of a person to an advertiser, they sell the eyeballs of a person who just asked a question about the product that advertiser sells. Google is selling the information about searcher intent and that is very valuable indeed.
There is a fun experiment you can run which can show you information pricing in action.
Set up a chessboard at some distance removed with the white queen on a certain square. At a nearby table, offer to pay someone $2 to go to the far off chess board and come back and report the position of the queen. As soon as its reported the queen is moved to a new position. Now an entrepreneur can walk down to the chess board and on his way back sell the information to someone coming the other way, walking less and getting a fraction of the value. A really creative entrepreneur can set up a web cam that watches the board and they sit there 10 yards from the source table repeatedly selling the new positions as they come in. In that respect they are doing what high frequency traders do, applying technology to achieve an information advantage which is then convertible into revenue.
Understanding how information develops value will illuminate the strategies that will capture that value. As more and more people figure this stuff out we will see more things like flattr.com and other services. For a long time I've been expecting a curation service to appear which does what an executive secretary might do for a busy executive, pull the the top 10 or 15 best articles describing that news of the day or the area of interest, and making those easily consumable on the go. Capturing the value of the information curated, versus a giant pool of information one is forced to forage through to get to the good bits.
I, too, have thought about a system like what you describe ($25 a year, distributed to each thing you visit). However, there are some issues.
1) You say 1/3 of a cent per visit... what happens after you visit 7,500 sites in the year? Where does the money come from at that point?
2) Say that instead of a 1/3 per year fee, you just take the whole $25 and divide it by the number of sites I visited...so if I visited only 5 sites in the year, they each would get $5, but if I visited 25,000 they would each only get 1/10 a penny. The question then becomes, how much is a reasonable amount to charge per year, if we are going to charge the same rate to everyone? Should someone who consumes much more pay more, or is it a flat rate?
3) No matter your system, there are going to be issues of content. Does a click-baity article that takes 10 seconds to read cost the same as a 10 page, in depth and well researched, article? You are going to incentivize people to make cheap and quick content, since you are not rewarded for anything besides clicks.
I also think your analysis of piracy being a result of pricing something above what it is worth to be a bit of a stretch; no matter what something is worth, if you offer the same thing to me for free, I will take the free.
To give an example: Suppose I was selling $10 bills for $10, and the guy next to me was giving away $10 bills. Everyone will obviously take the free $10 bills from the guy next to me - that doesn't mean I was selling the $10 bills for more than they were worth, it just means that people will always choose to pay less for something no matter what it is worth.