Why does Adobe not take legal action against websites that provide crack copy?

They do take action when they know about it. 

The problem with pirates is that most are offshore & out of legal reach of US jurisdiction.  Or they fade away for a time and come back later under different identity.  It's a cat & mouse game.

Pirate sites can only thrive because some people are greedy and don't want to pay legitimate prices for legitimate software.  If pirates didn't make money, they would vanish really fast. 

You can report piracy here: http://www.adobe.com/antipiracy.html

There's not much we can do. This is a public forum, not Adobe support. We're not Adobe employees (for the most part) and have no say in what actions Adobe corporate takes.