I appreciate you making your position clear. I'm actually really close to you on this issue (being a BIG fan of the defense of state's rights).
Can you think of any situation at all - even in the most extreme situation where a state government completely fails to uphold what it is supposed to do that would result in you being OK if the federal government stepped in? The reason I ask is whether this is an issue of subjectivity once again where there is a line that you would be OK to cross if we got to that point, but we're just no where near that point yet.
I can only think of situations where I mentioned ... discrete emergencies where great bodily harm or death is in play.
Everything else must go through the courts, or via an invite.
If you call 911 saying your neighbor said he's going to cut your tree down. They'll respond that
that's not an emergency, nor is it a police matter. They'll say it's a civil matter to be resolved in court.
But if you call 911 saying your neighbor has a gun, and he said he's on his way over to kill you. Now
that's an emergency, and the police will act.
The Fed, imo, are like the police in these examples. Their job should be to stay out as much as possible. If the locals, state police or national guard can handle it, let them. That's what they are there for.
If they courts can handle it, let them.
Problems, in every type of scenario, should be handled at the lowest level possible.
To your question specifically:
States don't fail, people do.
There are many parts to a state government. If the governor fails, the states representatives can impeach, or invoke immediate remedies and removal if medical professionals certify that the governor must be clinically crazy.
Those same representatives can pass emergency legislation to override a wayward governor and they can even
invite federal assistance.
I can imagine no scenario where a POTUS can examine crime statistics (or anything else), and decide on his own, to invade a state.
But I can see the Feds taking the lead when a federal question is in play (kidnapping across state lines, anything involving more than one state, basically). Local crime is not a federal question.
BTW, POTUS could instead be looking to enforce the guns laws that are already on the books. The guns in Chicago aren't manufactured there, they are going in from across state lines. That's ATF's jurisdiction.