Neither of your points is correct. I'll start with your second point since the situation there is more clear.
> As well, DMCA takedown notices are only supposed to act to take down the relevant content, in the case where the recipient of the notice (i.e. the user of the hosting provider) doesn't respond/contest the notice.
Actually, according to the text of the DMCA [1], a provider is supposed to first "inform[] that person that it will replace the removed material or cease disabling access to it in 10 business days", then "replace[] the removed material and ceases disabling access to it not less than 10, nor more than 14, business days following receipt of the counter notice".
They have to keep the content down for two full weeks after receiving the counter-notice. Yes, this is blatantly unfair. But that's how it is.
In practice, providers sometimes restore access sooner, but they're forfeiting the safe harbor by doing so.
> DMCA takedown notices are a sort of pre-trial motion, used only for a very specific "obvious" kind of infringement, to take it down in advance of suit.
I'm not sure whether the question of whether contributory infringement can be the subject of a DMCA notice has ever been tested in court. If you know, feel free to enlighten me. But I doubt it has, since the issue would only come up in a 512(f) lawsuit accusing someone of a fraudulent takedown, and that clause has barely ever been used at all.
From the text of the DMCA, though, a DMCA notice is supposed to contain, among other things (emphasis added):
> (i) A physical or electronic signature of a person authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.
> (iii) Identification of the material that is claimed to be infringing or to be the subject of infringing activity and that is to be removed or access to which is to be disabled, and information reasonably sufficient to permit the service provider to locate the material.
"An exclusive right that is allegedly infringed" is broad wording. And point 3 anticipates that the "material" might not be "infringing" but merely "the subject of infringing activity"; it's not clear to me what exactly the difference is, but this also suggests a broad scope of what kind of "activity" might be covered.
Admittedly, that's fairly weak textual evidence. But I don't see any language supporting the opposite position. At minimum the law is ambiguous. So unless it's been tested in court, I don't see how you can claim that DMCA notices are "used only for a very specific 'obvious' kind of infringement".