The way I see it is, why would a doujin artist ever want their content removed?
If I was a single artist looking to promote my work and I went around telling everyone to not post my content and demanded that people buy my stuff, I'd look like an a-hole and nobody would want to buy anything I make. Hell, there have been revolts from internet communities specifically because of that kind of censorship.
I think part of why Doujin content actually works is because they're not super strict about it. The idea is you share stuff together and build a community around that. If people want to buy the content, then they make the choice to do so. You can't force someone to buy your CD, it doesn't work like that, even though the system makes it seem like that's how things work. Consumers have free will, and are more likely to buy your content if you make it more available to them.
I think part of why so many youtubers DON'T buy Touhou Albums is simply because they didn't even know they could or where to buy them. A lot of common questions you hear on youtube are things like "What is this song from?"(even though it's in the description) or "Where do I get these games?" This is a simple problem of people not wanting to put the effort into buying things. We could change that by making it more corporate and strict, but would that really help the community? I don't think it would.
Another way of looking at this is, what about the background music in MMD videos? What about Nicovideo? What about people on Youtube who upload mmd videos? Does this apply to the whole internet or only Nitori's channel? I think it's fair to say that the channel wasn't take down fairly at all. It wasn't even for a video they still had up. I don't think Google will care about petitions, but I do think youtube needs to fix it's piracy system. It's clearly out of line and unfair to it's users.
I think what Nitori has done would have been done whether or not Nitori was the one doing it. People share this music because they like it and want you to have the option of buying the CD. If they cut the song halfway or made it hard to listen too, people would find someone else to follow who uploaded the whole song instead. I agree that piracy isn't okay and people should be encouraged to buy content, but that doesn't mean forcing it down their throats. On the forums here, it makes sense, and I'm willing to follow the rules on piracy, but on the rest of the internet...it's just not how it works.
Personally, I've bought Touhou games by ZUN and his books, along with music created by various artists and I really enjoy supporting them, but I can say I never would have gotten into Touhou, played the games, or even bought an album by a single circle if it wasn't for people uploading stuff onto Youtube/Nicovideo.
A good way to solve some of these issues would be to have circles make their own youtube channels, but I don't know if that will ever happen, especially because of the language barrier. I think we should support the community as best we can, and like some others have said, if someone does request a song removal, just take it down, no questions asked or if someone asks where to get the games or music, link them to a store or a good page for buying the stuff and help people to make the right choice.