I think you need to look at it from a different perspective.
Your point is that because at a mayoral level they're blue areas and they have a lot of crime, means Democrats somehow encourage crime with their policies.
Problem is they're not just blue areas. If the city is blue and the state is red, then you have competing politics.
Which is stronger, the city or the state?
The state, clearly.
Now, why is it that some of the worst cities are in REPUBLICAN states? Are you saying this has nothing to do with Republicans? That's absured.
You could play the blame game all day, and you'd never really come up with an definitive answer. What policies are causing cities with high crime?
Is it right wing gun policies, is it education policies which don't meet the needs of the people in those cities?
Take Detroit. The reason Detroit has such high crime is because of things like the lack of jobs. Well, that's because the auto-industry in the US is dying. Is that based around city politics? State politics? National politics? Probably the latter.
The problem in the US is a national one. It's about two political parties who control everything and play politics more than they actually run the country.
You can look to other countries and see that crime is higher in bigger cities. London is an example. It's not about left or right there because London has only had a mayor for a short amount of time, and the first was left, the second was right and not much has changed anyway.
The problem is a US problem that people are trying to hide from by saying it's this problem or that problem.
However some states have higher crime than other states. Why? State politics does play a part, and so too does city politics. New York, a liberal city, is a city that cleaned up its crime problem. But not without criticism of human rights abused.
I can explain how a red state can have a red governor and blue shitholes.
Blue voters have enough votes in blue shitholes to remain blue, but there aren't enough blue shitholes and blue voters to make the whole state blue.
If there were, the whole state would be a blue shithole.
And for your information local law enforcement has a greater influence over crime prevention.
Local government has a greater influence over economic development.
Blue shitholes are shitholes because they are blue.