With the obvious proviso that it would need to be simple enough for everyone to set up in order to get the traction necessary to be useful. Simple enough for everyone means one button with a single 'Yes please' screen (eg OAuth). Anything more complex than that is destined to fail.
And similarly, how do you prevent fraud? WAP was a walled garden experience; if I can send money to any site on the Internet by clicking a button, what's to stop a malware author from using their malware to send lots of clicks (and thus money) to a site they run?
Technically, micropayments aren't a difficult problem to implement. The business rules around financial transactions (which exist for good reasons) often present an intractable conflict with what would be a viable user experience.
Already happening with pay-pr-click ads etc.
Micropayments would be a different story since the money would be coming out of individuals' pockets.
I set up an account, put some money in it, set a $20 monthly limit, hook it up to soundcloud and github, and then every time I "like" a song or "star" a repo it adds them to that month's list. At the end of the month it divides the $20 between everything I enjoyed most that month.
A similar system would probably work for ALL web content. But as always this gives the control directly to the consumer and big companies don't like that at all.