This issue is solvable without having to close down these companies - they just need to change how they operate. Their very nature will always attract people who want to share illegal content, but right now they just make it way too easy.
Many don't require accounts for downloading, there is little to no verification on uploader accounts, next to no content verification..and so on.
Simple things like requiring an account to access a file, or even better to require the uploader to share files with an account (Rather than to a group or the public) would make it much more difficult for them to be used for warez.
It's not a new problem - heck back when i was involved in some HTTP sites (as a naughty teenager..I am reformed now) we had tools that would go and create a few hundred Geocities or Tripod accounts for us to use for uploads - they were so easy to create and use as they had no verification apart from a captcha (which are useless in real life..so easy to defeat). Those accounts stopped being useful because of the file size limitations (10mb max
iirc) and because yahoo/tripod got really good at spotting these accounts.
I don't know how these services are used today but I imagine it's on the same lines. More use of account filtering and content tracking would make a huge difference and allow the sites to be use legitimately as well as being used by pirates.
There is a fine line between ease of use and blocking piracy - but at the moment these sites are becoming almost as much of a problem as bit torrent sharing - if not moreso as you don't even need half a brain to use them, at least with BT you have to install a client.