If it went to court.
The only known case linked was 2009, which Blizzard won because the private server was shown to directly prevent customers from purchasing TBC. As a secondary factor, the site was also located in the USA (same jurisdiction as Blizzard HQ), so the risk vs. reward was justified to pursue.
If Blizzard really want to go to court, perhaps they could try. But they aren't trying now are they. Oh but we do love backseat lawyers on this site
By all means continue telling us what they should do, as they stand with professional lawyers and continue to do nothing.