You're supporting the future generation of developers and game managers that might someday work in your company and make you millions more. Even if not, the most a server can make is a few thousand, and you'd be making a few million.
You spend a million on a lawyer to take down private servers, and most of these servers can only offer you the few thousand that you've earned, and the players who might have played both the server and your official server might quit your official server due to rage, and people who might have played the server because it's the first time they've heard of the game lose the good impression that they got from the server. Chances are that some of those players could have potentially earned you much more than you would have earned if that server had not existed in the first place.
You have a lot of free advertisers that spent a lot of hard work and their own money at no charge to you, and those advertisers are of the same age group your company is advertising to. Their ads would be much more effective, and once they are hooked to the private server they might be curious about the official server. This would make up for the number of disgruntled players who left the official server for the private server, over and over. These disgruntled players would have quit anyways, and due to the server, they still like the game, and that gives the company a chance to fix their ways and earn this player back.
/wall of text
The only con to them is if their official server sucks so bad that the players who were only looking for a temporary place to stay while the official server was fixing up eventually just give up on the official server. But again, they probably would have quit anyways.
