What citizens would trade their own police force for one known to be corrupt to the core? That’s asking to import violence into their previously peaceful towns. You are basically asking to spread the disease everywhere; this is not a cure.
Only if you're not paying attention.
Corrupt departments getting swapped out for others limits their impact in the affected region. The same principle is at play at the next location.
Additionally: corruption thrives (e.g. in the first location) because it has the necessary preconditions to tolerate it; courts and the local folks at the next location are not going to take up a passive posture if the new guys show up and their town is plunged into corruption.
Both factors should lead to the corrupt departments being discouraged to the point that they recognize the futility.
Alternatively, you could limit it to only swapping out the LA units for the ones that were in Idaho, sending the LA ones nowhere—they're just gone. The problem, after all, is the inability to get rid of all law enforcement headcount in an entire region, even if it is by and large thoroughly corrupt. The Idahoans coming in make that a non-issue.