Frankly, elected officials do not trust bureaucrats. This is quite justified. You mention above judgement, intentions, expertise ad competence. This is not the trust issue.It is up to the elected official to set policy. Many times, the bureauracy attempts to thwart those policies. This is well documented. I was re-reading Henry Kissingers memoirs recently for an article I was working on. The motivation for their backchannel diplomacy was that the bureauracy in the State Department was actively trying to thwart their efforts. It is a good thing that they were successful in their efforts.
There are other reasons for elected officials to be distrustful that have nothing to do with policy. Any bureauracy (government or business) tends to be self centered. Calls by people who have experience in the commercial world to apply methods such as six-sigma to the bureauracy are just a recent symptom. This requires, by the way, completely changing (or throwing out) the current civil service system. I live in the Chicago area, and we see terrible waste and corruption in the city. On the other hand, the schools in the suburb I live in are doing very well, while spending perhaps two thirds of what they spend in the city. I guarntee you that our facilities are better, and our teachers and administrators are well paid.
A related issue is the interplay between elected officials, bureauracys and fuding can raise issues. We also have in the Chicago area Argonne National Labs (ANL). This is a national energy research facility. I have several friends and neighbors that work there. Many are PhD’s. I ca tell you that they do a lot of research that is not energy related. When I discuss this with them they become defensive, and for good reason. We have lots of energy issues that could be addressed by basic research, but we are not using the resources we have. One of my neighbors was working on fuel cells. Last I heard, he was looking at the river bed under bridges. This is not his fault or choice. I am sure it is a way to keep the group he is in employed. On the other hand, this is another example of the bureauracy not addressing the issues that face the country, but working to keep funded. This ia a big mess and it requires a whole rethink of the system.