You say that, but I've already posted numerous times in this thread exactly what the FBI could and should be looking into that would either bolster (if not outright confirm) or contradict the claims made against Kavanaugh.
Here's the problem - you, among other posters in this thread, are looking at this entire situation almost perfectly backwards. This isn't a criminal case and Kavanaugh isn't on trial. He has no constitutional right to a Supreme Court nomination, whereas a defendant in a criminal trial has the right to his freedom unless convicted beyond a reasonable doubt of a criminal offence.
What this is is a job application. Kavanaugh is, in essence, applying for a new job with lifetime tenure and an extreme level of power and responsibility. He is entitled to an assumption of innocence, but only to a point; if credible allegations arise against him, the burden is on him to disprove those allegations to the satisfaction of his interviewers and the people he represents (and as I write this, The Guardian has indicated that they have heard from a third woman who is planning on coming forward with allegations against Kavanaugh - the judge's job to clear the cloud of doubt hanging over him is getting more difficult seemingly by the hour). Certainly, if I was applying for a job and someone said "Hey, we checked your references and your past employer said you had a habit of stealing office supplies", I would not be saying "I was never charged with or convicted of anything" - I'd be telling them exactly why the allegations were spurious (maybe I had a terrible boss and we parted on bad terms or something) and trying to find proof to bolster my claims (like other employees who went through the same thing).
I will say this - if I was in Kavanaugh's shoes and women were coming forward to accuse me of acts I did not commit, there would be no one screaming louder for an FBI investigation than me. Because even if their claims were flimsy, I would want all doubt erased as to my good character. The fact that Kavanaugh is not stridently requesting a thorough, in-depth investigation speaks volumes.
That's never how burden of proof works. Burden of proof is ALWAYS on the person making a claim. ---