A: Hosting companies are not held accountable for hosting illegal content if they cooperate with authorities. There are specific procedures for the gamut, including child pornography. The FBI is very active in working with established hosting providers to investigate and take down illicit and illegal content.
B: Your suggestion would shutter smaller startup hosting companies, raise prices at others, and cripple the startup community that Hacker News loves so much. The fallout from your suggestion would be so colossal that the harm to innovation from software parents would look minuscule in comparison. Should we punish the telephone company for every bomb threat that traverses the line? Dreadful.
B: you're misinterpreting what I said, which was rather: "Should we punish the telephone company for unilaterally disconnecting the line of people accused to send bomb threats, regardless of whether they actually did use it that way?" And my answer is hell yes. At the moment, ISPs pay no penalty for screwing the innocent, unlike the other two parties in the law. I don't think that's reasonable.
The third party can file a counter notice, at which point the second group has no legal obligation to screw the third, nor has any legal liability in not screwing the third. What am I missing?
You have a system that, de facto, introduces incentives for ISPs to disconnect, but no incentive for them to help an innocent third-party or even just carry out due diligence.
There is indeed a (rarely exercised) chance for site owners to get back at "malicious rightsholders"; however, there is no real accountability for hosting companies, which are then free to "err on the side of caution" (i.e. quickly pull as many plugs as possible to avoid a costly lawsuit). This should probably be rectified: hosting providers should be held accountable for unwarranted terminations as much as they are held accountable for hosting illegal content.
One could say that "the market will hold them accountable", but looking at the increasing frequency of this sort of takedown shenanigans, I'd say that's a naive view.