The idea is simply to avoid conflict of interest, and as you know and described, that is inherent when the executive investigates himself through one of his people. We do the best we can.
My view of the impeach vs. criminal charge issue is that the question is academic. If there was evidence that the president murdered a judge, the crisis gets managed somehow and the details aren't all that important. I think the correct approach is impeach and remove him first, then indict him. But I don't think it matters if the order was reversed. The difference amounts to a certain amount of shuckin' and jivin' in motions before the judge.
Impeachment itself is a political question. It does not follow the usual spectrum from articulable suspicion to probable cause to (whatever the standard is for indictment) to beyond a reasonable doubt.
But your reference to the standards of evidence is interesting, because from what I can tell, there is ZERO articulable suspicion (the lowest level) that the Trump campaign was involved in campaign coordination with anybody in Russia. The suspicion is "from the imagination," taking disjointed facts, and coupling them on the basis that Trump won the election. If he had lost, the investigation would not exist. OTOH, if there was a crime, and he lost, the investigation would persist.
The idea is simply to avoid conflict of interest, and as you know and described, that is inherent when the executive investigates himself through one of his people. We do the best we can.
Unless someone comes up with something better, I think the "best we can do" is remove the prima facia conflict of interest by having the executive branch officers investigated by appointed officers of the House.
This Trump thing also make it important IMO to clearly define the steps required to bring about valid impeachment (formal charges), or else we get prima facia conflict of interest and "guilt by accusation" as the Lying Left is trying to do here.