The Pirate Bay is a very unique case because:

1. Hosting costs are very low due to the inherent nature of torrenting. It's essentially just an index of magnet links used for downloading torrent files. Apparently the whole TPB directory could fit on less than 100MB of storage. They don't actually host any of the illegal content they provide.
2. They've hosted the site on multiple cloud services, which law enforcement would have to play an endless game of whack-a-mole to truly dent.
3. Sweden are notoriously lenient on piracy and copyright infringement. TPB's founders only faced a year in prison and a hefty multi million dollar fine when they went to trial.
4. United States authorities are very unlikely to get the Swedish courts to extradite these individuals, because their 1960 extradition treaty is quite strict on what offences one can be extradited to the USA for, and the only mention of piracy on there refers to the maritime kind. Compare this to how easily Kickass Torrents was taken down and how the Polish authorities nearly got its founder flown out to the US to face trial.
5. The hosts not only provided the knowledge to but outright encouraged others to host mirrors/proxies of the website to get past DNS censorship.
6. There are ways to detect CSAM which makes it a lot easier to track down and lock up individuals who access it. Another big difference is that producing, distributing, and even possessing CSAM is seen as a far more heinous crime against humanity than downloading a pirated movie copy.

TLDR: there are three things that could survive a nuclear armageddon: cockroaches, Keith Richards and the Pirate Bay.