a) should online speech be policed
b) if so, who should do it?
We don't let phone companies police the content of phone calls, and we don't let delivery services police the content of letters/packages, so why would we let ISPs police the content of network packets?
Exceptions exist: you can't send most live animals by mail, packages are subject to inspection at customs borders, etc. But any sort of monitoring of content would need either clear evidence of danger, signs of abusing the network, or court involvement.
If this content is so terrible that it deserves to be removed from the internet by any means necessary, shouldn't the process be that a court of competent jurisdiction should be able to issue an order requiring the site to be taken down. If the proprietors of the site bring it up through another ISP, not a party to the original order, a new order could be issued as well as holding the proprietors in contempt, presumably.
Jurisdiction issues on content are hairy, but jurisdiction issues on ISP connections are easy, the connections happen in specific locations, and you can order the connection severed at either end of the connection (as well as in between the ends).