Why does there have to be a compromise? Please don't take this as some sort of flame bait. Instead it is a serious question about why some advertising must exist and be tolerated.
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.