No, you just said it yourself "why should the doj have to start over when much of the investigation has been done?" or something like that.
If the house does all the work and then turns it over to the doj, and the doj says "thanks, well just use all of this in our investigation", how is that different than the house just doing the investigation themselves? If the doj can just use the house information, then why even have the doj conduct an investigation? It's already been done. The house would then just tell the doj "here's the investigation, wrapped up in a bow for you" and the doj could just take that and start handing put indictments.
However, I hope the doj does the investigation, then someone other than dems will have subpoena power. If Trump has committed these crimes, then he needs to answer for them. However, if after 7 years of dem committee investigations, and then a doj criminal investigation, and they STILL can't find anything to pin on Trump, then the dems will be responsible for making Trump the MOST vetted presidential candidate in history...