Wouldn't it be smart for CBS or Paramount to just make a deal with or take over Star Trek: Phase II and/or Star Trek Continues as a way to get Trek back on air in some media or other? They both are quality fan series and at least Phase II has a fan base that could be built on which could somewhat negate the economic difficulties a brand new Trek series would face.
Fan series get away with what they do because CBS technically turns a blind eye to their efforts. If a fan group got too much notoriety; CBS WOULD need to issue a 'Cease & Desist" order to protect their copyright on the IP. (If they do not, then it can be claimed in court that they no longer have IP rights to Star trek because they must show they are legally 'enforcing' and 'protecting' their claim, or they lose it and it slips into the public domain.)
Many people like to think they are 'afraid of angering the fanbase' - but that's not the case; as honestly 99% of the fanbase doesn't know about or really care about fan efforts.
As to why they don't just 'take over' - once they are publically involved; such a series would be governed by AFTRA and other entertainment union rules, with regard to who can work on such a show, pay scales, etc - so costs would rise to the level of a professional production.
fan series survive because as far as CBS is legally concerned, CBS is essentially claiming: "We have NO IDEA this is occurring with our Star Trek IP."