The question that remains is whether it is sufficient. Many observers are withholding judgment until the special prosecutor is chosen. Recently, it has been the personal reputation of the official to whom decision making has been delegated that determines whether an investigation is deemed credible. Sometimes, the inevitable assertions about the chosen investigator's integrity corresponds with popular perceptions about the outcome (for instance, the decision to prosecute "Scooter" Libby for blowing the cover of an officer of the Central Intelligence Agency) while in other investigations, the perception of the impartiality of the investigation has remained in dispute after its conclusion (e.g. FBI Director Comey's decision not to recommend that the Department of Justice seek an indictment against Hillary Clinton for mishandling classified documents).
The reason why the identity of the investigator matters is because these so-called recusals are really only half-recusals -- the official who is operating under the conflict of interest (and/or their superior, the president) continues to maintain ultimate authority over the person they delegate (or whom their delegate chooses, e.g., the special prosecutor who will be chosen by Sessions' Deputy Attorney General, another presidential nominee). At the end of the day, if the special prosecutor has a reporting line that runs to the president, the President can influence the investigation. Even if the investigator really is incorruptible, the President can fire them, and the official who appoints them has a clear incentive to find someone with that reputation but who is in actual fact sensitive to the pressure of termination or other career-ending tactics.
This is exactly what happened when the Watergate investigators came to close to uncovering evidence of President Nixon's wrongdoing, after following a trail that passed through an indictment of Attorney General John Mitchell. Two months after Mitchell's indictment, Nixon commanded his new Attorney-General (and then his Deputy after that official refused) to fire Special Prosecutor Archibald Cox. Ultimately, Cox was fired by Solicitor-General Robert Bork after Nixon promised to reward him with a nomination to the Supreme Court (Bork was in fact nominated for such a position before that corrupt bargain was revealed; after his nomination failed he returned to his lifetime appointment on the seat of the nation's second most influential court, the D.C. Circuit). There is always an executive branch official that will comply with an order to end an investigation.
There was a solution to this problem, and Congress adopted it in 1978. The Ethics in Government Act set up the Office of Independent Counsel, which created a system where the special prosecutor would be selected by a panel of judges and could only be dismissed after a showing of good cause. They would then be empowered to investigate senior executive branch officials (and those involved in presidential election campaigns) with no limitations on the budget or where the investigation might lead.
Unfortunately, that office was abolished in 1999, and replaced with the toothless Office of Special Counsel, which operates under federal regulations that the executive can amend at will, and which also establish that "the Attorney General may request that the Special Counsel provide an explanation for any investigative or prosecutorial step, and may after review conclude that the action is so inappropriate or unwarranted under established Departmental practices that it should not be pursued." The Attorney-General can also terminate the Special Counsel, as was the case in the Saturday Night Massacre.
It is unclear why Congress decided to give the executive back this power. It is particularly unfortunate, as the investigation of Sessions bears substantial similarities to the investigation of another of Nixon's Attorneys-General, Richard Kleindienst, who was ultimately convicted of withholding information from Congress during his confirmation hearings. (That said, there are important differences between the Kleindienst and Sessions allegations, particularly as Sessions was serving as a Senator at the relevant time, which invests him with the immunities created by the Constitution's Speech and Debate Clause).
It is unlikely that the allegations against Sessions will ever receive an adequate appraisal. The abolition of the Office of the Independent Counsel politicizes every investigation of executive branch officials. Instead of discussing the legal standards and the boundaries of executive accountability, the press and public are reduced to discussing the character (or personality, or political affiliation) of the investigators and of those arguing that they exceeded the scope of their authority, as was the case during the Hillary Clinton email controversy. Ultimately, the only decision that the public can make is about whom to trust. This is precisely the kind of argument that a political strongman likes to make, and which the rule of law was designed to pre-empt.
A return to legal norms requires the reconstruction of legal authority. A pastiche of justice merely erodes popular confidence in the possibility of apolitical justice; this is what allows Trump to make more arguments about how all the opposition is merely partisan.