Your belief that it is "not a counterintelligence" investigation is based on what? Genuinely curious, since that is inconsistent with Rosenstein's letter.
Criminal investigations are undertaken when investigators have a good-faith basis to believe one or more penal laws may have been violated. They target a particular person (or persons in the case of concerted criminal activity). Once investigators are convinced that a crime has been committed by the suspect, the objective of the investigation is to build a case fit for prosecution in a court of law (to amass sufficient evidence to prove the essential elements of the statutory offense beyond a reasonable doubt). The investigators fully anticipate making a formal public charge against the suspect (an indictment), which will be followed by a public trial -the presentation of witness testimony and evidence in a judicial proceeding open to the public.
Obviously aspects of criminal investigations are secret; warrants and wiretaps would not be very useful if police had to notify the suspect in advance of their raids and surveillances. It would be very difficult to get the cooperation of witnesses or compel the production of relevant documents if grand jury proceedings were conducted in public. Most significantly, the suspect is presumed innocent. To publicize investigative information before a person has an opportunity to test its credibility under due-process rules would undermine the presumption and brand the person a criminal.
This is day-and-night different from foreign-intelligence investigations. The objective of the latter is not to target a particular person for public prosecution. It is to protect the security and interests of the entire nation of American people by acquiring information about the actions and intentions of foreign powers.
Virtually everything involved in a foreign-intelligence investigation (its existence, any attendant court process, the information gathered, the analysis of its meaning, the methods and sources of its acquisition is classified). When the information is collected, the presumption is that it is only for the eyes of government agents responsible for protecting national security and other American interests. In fact, even within that “community” of intelligence operatives, the information is closely held.
Citizens who are caught up in foreign intelligence investigations are generally not suspected of criminal wrongdoing. If they were, they would be subjects of criminal investigations. The government is not supposed to use its foreign-intelligence collection authority as a pretext to build criminal cases. Consequently, there is an emphasis in intelligence investigations on maintaining the confidentiality of citizens whose identities or activities cross the government’s radar screen. Generally, their identities are concealed (or “masked”) even from intelligence agents working on the investigation. The investigative relevance of these citizens lies not in their own conduct, for the sake of proving them guilty; it lies in what their conduct (whether knowing or inadvertent) can tell our agencies about the plans of foreign powers that could imperil our country.
Therefore, the presumption is that foreign-intelligence investigations do not and should not become public -the opposite of our presumption for criminal investigations. Indeed, before FBI director James Comey’s startling public revelation (in congressional testimony) of an active investigation of possible ties between Trump associates and the Putin regime, what we knew about the investigation came from the leaking of classified information —a felony.
Mueller's witch hunt features elements of a criminal investigation; public indictments, plea bargains disclosure of evidence and highly publicized judicial sentencing (not features of counterintelligence investigations). Nonetheless, there are also plenty of sealed indictments and other proceedings secretly held (more appropriate for a counterintelligence investigation). None of the publicly available material (except reference to 13 Russian purported GRU agents and 3 presumably also Russian "front" business entities (involved in an apparently insignificant social media disinformation campaign) has any nexus with any foreign power.
From what is available to the public Mueller is engaged in a
criminal investigation (or witch hunt).