This attitude goes way back. It is characterological. See the Fugitive Slave Act versus states' rights.
Also, the Democrats have never had a politician of any stature, let alone a president of their party, say "Government is not the solution to the problem. Government is the problem." That was Ronald Reagan.
In other words, you are right, the left does distrust those portions of the government it does not control, but there is an enormous difference of degree in how the two sides behave towards these portions of the government.
There's no inconsistency in trusting a democratic process to do mostly democratic things but thinking the lack of accountability in policing has had negative outcomes. The vast majority of democratic voters in america do not support "abolish the police' in entirety, but rather that reforms are needed.