As the Senate moves this week toward voting on the creation of a 9/11-style commission to investigate the Jan. 6 attack on the Capitol, Republicans have raised a series of arguments against it. They have objected to the inquiry’s scope, its length and even the process for hiring its staff.

But last week, announcing that he too would oppose the plan, the Senate minority leader, Mitch McConnell of Kentucky, made another argument: He claimed that the commission was redundant, noting that the Justice Department and congressional committees are already looking into the assault.

“It’s not at all clear what new facts or additional investigation yet another commission could lay on top of the existing efforts by law enforcement and Congress,” Mr. McConnell said.

What he failed to mention was that the criminal investigation into the riot, despite being one of the largest in American history, was narrowly bounded by federal law and would not — indeed could not — seek the answers to several crucial questions about Jan. 6. The same can be said about the major congressional effort to investigate the assault, a tightly focused inquiry into the broad government response to the violence that day.

Here is what the current investigations can and cannot do, and what an independent commission might bring to the table.

The political roots of Jan. 6

One of the complexities about the Capitol attack is the inextricable link between criminal activity and legal behavior protected by the First Amendment. After all, the riot took place after — and was in part incited by — rallies led by figures including President Donald J. Trump, his lawyer Rudolph W. Giuliani and his onetime adviser Roger J. Stone Jr.

In the early days of the Justice Department’s investigation, there were scattered signs that prosecutors were looking for information about some political activists who organized protests that preceded the attack.

In January, for example, the F.B.I. searched the homes of two men from Southern California, Alan Hostetter and Russell Taylor, who appeared with Mr. Stone on Jan. 5 at an election protest event outside the Supreme Court. Mr. Stone himself also came under scrutiny at one point, prosecutors said, as the authorities examined communications between him and right-wing extremists who breached the building.

But those efforts have not resulted in any charges, and there is no public evidence that prosecutors are still investigating the political roots of Jan. 6. One challenge is the tools they have at their disposal, like search warrants, which require proof that a crime may have been committed. An independent commission, armed with subpoena power, could more easily compel testimony from political operatives who may have knowledge about Jan. 6, even if they did not clearly break the law.

“Criminal investigators are only supposed to investigate crimes,” said Joel Hirschhorn, a veteran defense lawyer who has represented several clients charged in political riots. “But a commission is better suited and better able to look at the political reasons behind Jan. 6.”

The question of motive

As many as 500 rioters may face charges in connection with the Capitol attack, prosecutors have said. Many questions will eventually be answered: How did all of those people get to Washington on Jan. 6? What exactly did they do on the grounds of the Capitol? And what happened once they went back to their homes?

But one important question, crucial to understanding the events of that day, is not likely to be answered — at least not by the government — even in the hundreds of cases. And that is why those charged with crimes took part in storming the Capitol.

While the issue of motive is a staple of police procedurals on TV, it is less important at actual trials in real-life courtrooms. Defense lawyers may decide to discuss their clients’ motives with the judge at a sentencing hearing in an effort to reduce potential penalties, but prosecutors in their public statements are much more likely to stick to the facts of who did what when rather than delving into why they might have done it.

“In criminal prosecutions, the issue is generally one of behavior inferred by circumstance and corroborated by evidence like documents, emails and cooperating witnesses,” Mr. Hirschhorn said. “Motive is never really an issue when the government is trying to make its case at a trial and prove guilt or innocence. It’s just not relevant.”

The big picture

Even though prosecutors have charged an unprecedented number of people in the riot, that does not mean they are looking at the big picture — exactly what a commission would be asked to do. Indeed, at the urging of judges and under pressure from defense lawyers, investigators in the inquiry have taken pains to treat each of the 450 or so people charged so far as individual defendants.

“The job of a prosecutor is to prosecute the cases directly in front of them, not to zoom way out and give their views on the totality of the events in question,” said Alan Rozenshtein, a former Justice Department official who now teaches at the University of Minnesota Law School. “It would go against their training to just start freestyling in a courtroom about the broad state of American democracy.”

Even if prosecutors did want to provide a panoramic view of Jan. 6, they would not have much of an opportunity, Mr. Rozenshtein said. Many, if not most, of the Capitol defendants are likely to plead guilty in the weeks to come and avoid a trial where their stories would be told in full.

“With so many plea agreements,” Mr. Rozenshtein said, “there will never be a complete exploration of the facts and issues with witnesses and evidence.”

Congress is investigating, but only narrowly

When Republican senators say that Congress is already studying Jan. 6, they usually have one particular inquiry in mind: a joint investigation by the Senate Homeland Security and Rules Committees.

That investigation is no small undertaking. It is bipartisan — a rarity in today’s Congress — and together, the two committees have oversight jurisdiction to look at the Capitol Police, the Defense Department and the broad government response to the violence. They plan to release a modest report about their findings and recommendations to secure Congress in early June.

But the scope of their work is tightly focused on questions of security and policing, rather than on what fueled the mob in the first place, what role Mr. Trump may have played and how the government coordinated its actions. The congressional investigators have also given themselves about only four months, meaning they will necessarily leave behind valuable information, and the dozen or so staff members involved in the investigation are also responsible for maintaining the committees’ regular work at the same time.

“There’s plenty more work to be done, and the more folks that are engaged in it, the better,” said Senator Gary Peters, Democrat of Michigan and one of the committee chairmen leading the inquiry. “They’re going to have more time and staff resources, and a commitment to do a real deep dive.”

Across the Capitol, House committees are taking a more scattershot approach, looking separately at domestic terrorism, the Capitol Police and intelligence failures. Speaker Nancy Pelosi has signaled that she could authorize a more comprehensive investigation, including the formation of a select committee, should the push for an independent commission collapse.

Government watchdogs are also at work.

Decades ago, Congress created a slew of independent inspectors general and embedded them in executive departments across the government as a kind of fail-safe against efforts to cover up wrongdoing or institutional failings. A handful have confirmed they are conducting investigations related to Jan. 6, but they are also taking narrow approaches, circumscribed by their jurisdictions.

At the Pentagon, the inspector general is taking a deep dive into two crucial outstanding questions about the riot: when the White House and Congress called for backup military support and why it took so long to arrive.

The Justice Department’s inspector general is looking at what federal law enforcement knew in advance of the attack as it collected intelligence about possible threats, and whether that information was properly communicated to those who could have prevented it.

And the inspector general of the Capitol Police has produced reports documenting in detail the breakdowns within the force as it battled for and lost control of the Capitol. The office is preparing to issue another report in the coming days on the department’s emergency response team and another after that looking at radio communications on Jan. 6.