You may substitute "commercial ad" every time you see the word "ad" in discussion about this, if you'd like to be picky.
It can go too far the other way, though. I heard that some of the "Pink" products gave a fixed fee to breast cancer, so buying their stuff wouldn't give any money. Others gave a tiny portion.
I'll concede that it's a good model for wikipedia - spend nothing, and nag users for donations. But it's not a great model in general. But it only works as a replacement for micropayments, and that's where unobtrusive advertising works better.
You can argue that users will be able to distinguish between the ads and the content, but Wikipedia serves a very diverse community -- children, the elderly, people who can't read very well, people who are more-or-less computer illiterate. If even a small percentage of them are confused by the ads, Wikipedia will have failed in a small way.
(FWIW, I've seen technically-literate peers get confused by the current banner too, thinking the person pictured was the person the article was about.)
It's much more difficult to detect and evaluate bias within the text of an article. There is plenty of this on Wikipedia now, usually because of partisan or ideological edit wars on lightly read articles. And it's getting worse as more and more barriers are erected to casual or first-time editors.
It is almost impossible right now for someone viewing an article for the first time to improve it, even with cited sources. Regardless of quality, the changes are frequently reverted quickly by a bot or someone squatting the article. To get a significant addition or change to "stick" requires a large time investment and knowledge of the arcane rules of appeal within the growing Wikipedia bureaucracy. Result: most people don't bother.
This, to me, is a much larger problem of bias than what you describe. I actually think ads could help this problem by decoupling the content from the money. Right now a relatively small group of people are the most powerful editors AND the largest donors. Wikipedia is at risk of becoming captive to a set of people who think it is "theirs."
Business is hard, and it's a different kind of hard than charities normally deal with. Being good at 2 things is more than twice as hard at being good at one thing, so I think charities are wise to generally stick with being non-commercial.