To my mind, just as Mueller did with several investigations, when it found evidence of any wrongdoing that did not fall within the scope of his investigation, he referred the evidence to the appropriate bodies to continue prosecution.
Robert Mueller specifically said that this was not what he was doing. The Washington Examiner quoted Mueller as saying:
Now before we go to questions, I want to go back to one thing that was said this morning by Mr. Lieu, who said, and I quote, ‘You didn’t charge the president because of the OLC opinion.’ That is not the correct way to say it. As we say in the report, and as I said at the opening, we did not reach a determination as to whether the president committed a crime. With that, Mr. Chairman, I’m ready to answer questions.
I.e. they did not refer it for prosecution. They referred it to determine if prosecution or further investigation or nothing should occur.
It's also worth noting that what they were investigating was two matters:
- If Donald Trump or any associate of his engaged in a criminal conspiracy with the Russians to interfere in the United States elections.
- If Trump obstructed justice by interfering with that investigation (which predated the appointment of a special counsel).
So such wrongdoing was specifically within the scope of the investigation. Moreso than some of the crimes for which he sought indictments. In particular, Paul Manafort was convicted of neither criminal conspiracy of election interference nor obstruction of justice in that investigation. His conduct was unrelated to that investigation, but Mueller charged (and convicted) him. Also, the twenty-five Russians were indicted on charges of interfering but not on criminal conspiracy.
Trump is the only one with that particular protection. If they had found someone else had participated in obstruction with Trump, then they could have indicted that person. They did not do so. If there was any obstruction of justice in this matter, Trump did it entirely on his own.
There is nothing stopping the House from impeaching Trump. They could do it purely on a party line vote if they wanted. If they do not do that, it is either that they don't believe his actions warrant impeachment or that they don't believe that they convince enough of the public that his actions warrant impeachment so as to pressure the Republicans in the Senate to join in removing Trump from office.
If the House chooses to do nothing, that is of course up to them.
It's also worth noting that the typical Democrat does not really want Trump impeached for obstruction of justice. What they really want is for Trump to be impeached as a racist demagogue. But they are willing to settle for obstruction of justice. Of course, Trump was just as racist and just as much of a demagogue when he won the election. They should have done a better job of convincing people that was important then.
Impeachment of a president reverses the effect of an election. It is deliberately difficult to accomplish. It is supposed to require broad support from across the political spectrum.
The basis of the Office of Legal Counsel opinion that a president can't be indicted is that if a president could be, the president's opponents could just continually put a president on trial. And there is strong evidence that that would happen. The impeachments of Andrew Johnson (and later Bill Clinton) showed that partisan reasons will dominate.
The previous independent counsel statute, which was passed after Richard Nixon's travails, was allowed to expire because it led to the Kenneth Starr investigation, where Starr harassed President Clinton for the remainder of his term. Clinton would eventually plead guilty and turn in his law license. The reason why it was allowed to lapse was that this was widely seen as a waste of time and money.
Presumably if a new office were created, the next people to be able to use it would be the Republicans, just as happened last time. Then it would be abolished again and we'd back to where we are now.
If you want greater oversight by Congress, a more powerful tool would be to allow them to prosecute contempt of Congress. As is, they have to rely on the executive branch to do that, and funnily enough, it doesn't seem interested in helping investigations into itself. Contempt of Congress prosecutions would cover things other than potentially impeachable offenses. Of course, we might soon discover that that too can be abused.
My personal solution would be to create (via constitutional amendment) an Auditor General post that is always elected by the losers in the presidential election (in 2016, that would have been the voters for Hillary Clinton, Gary Johnson, Jill Stein, and everyone else who wasn't Trump). The Auditor General would run a shadow government, explicitly including the Inspectors General. Then the next time the government shifted hands, there would be an experienced core of people for the new government. And some of the exiting people could join the shadow government. But that's less an alternative to impeachment and more an improved review of budgeting matters.
I wouldn't expect it to change anything here, except that it would have prevented the actions that people are saying were obstruction of justice. Because Trump would not have been able to fire the investigators. James Comey would not have been involved in the investigation after Barack Obama left office. So Trump firing him couldn't have been construed as obstruction of justice. Trump would have been unable to fire Mueller.