Fair point, but it's not a restaurant and educating readers this etiquette would be really tough. How about pay for reading and refund if you think it's not worth your money? Would you do that?
http://i.imgur.com/YpuvdlX.png
If I ran a blog I would include the same element, some wording like "you know, creating quality content requires more effort than spewing clickbait, mind leaving us a tip to let us know that you appreciate our efforts?" and a flattr button.
Although your idea sounds like a good starting point for a website which caters to a massive audience (basically, every news website).
It's not a bulletproof idea of course, can be gamed. Users could take a screencap, or copy-paste, before the timer is up. But that's probably not worth worrying about until the model becomes widespread.