Running a website costs money. Some people also want to make profit, but that's beside the point. Micropayment solutions at present are sadly lacking - especially for international audiences. Don't forget also that you and I are a technical audience; I know at first my mother thought that websites got a split of her ISP bill when she viewed their pages. So advertising bridges a lot of these gaps.
Instead it is a serious question about why some advertising must exist and be tolerated.
I don't believe anyone is saying that you must tolerate advertising :-)
There is no answer to why advertising must exist aside from it being the best answer we have to a growing problem of who's going to pay for the Web. I'd rather have a few ads than fork out money on a package-basis a la cable channels.
If the majority of people with internet access preferred to pay directly for every website they use, advertising wouldn't exist. But they don't, so it does.
What about https://flattr.com/ ? It seems to be exactly, what you're looking for but haven't really taken off.
>Starting with Adblock Plus 2.0 you can allow some of the advertising that is considered not annoying. By doing this you support websites that rely on advertising but choose to do it in a non-intrusive way. And you give these websites an advantage over their competition which encourages other websites to use non-intrusive advertising as well. In the long term the web will become a better place for everybody, not only Adblock Plus users. Without this feature we run the danger that increasing Adblock Plus usage will make small websites unsustainable.
Part of me is extremely disappointed ABP made this change, but part of me knows there's got to be some compromise between absolutely no ads and annoying, intrusive ads. Not every website can offer a pay service. I'm happy they're making this change with small website owners in mind, and I'm also happy they're allowing users to turn off all ads by going in to settings.