Well, the Prime Directive is in alot of ways a self preservation issue. Because of our interference in other dimensions;
1. Smiley and the Terran rebels stolen the plans for the Defiant
2. Kidnapped a Federation citizen
3. When the Nagus was held in the Mirror Universe, it resulted in a Klingon cloaking device being stolen
4. One of the Orbs nearly got stolen
Having our (Prime Universe) tech stolen can not only change the outcomes of events in the Mirror Universe, but could effect the outcomes of this universe eventually.