Yes you're correct on all comments.
Other thing is that Britain and the US (relative to the world) have, by and large, honest and uncorrupt police forces. This is rare.
The Soviets attempted to cover up that there was even a serial killer at all in the case of Chikatilo, and the police were pressured to lay off him since he was a good party member.
In many countries the police would cover up the existence of a serial killer and make murders look like isolated occurances, to make their own life easier and avoid scrutiny.
Well, I would have to disagree with the accuracy of those remarks. In many nations with a very low homicide rate, and an all but nonexistent serial homicide rate, there is no basis to suggest that they are just more likely to get away with it and not get caught. Aside from the fact that a string of very similar and related murders would be a sensational event, they're police forces are just as effective if not more so than the US. By example, Japan and Germany pop to mind.
It's also worth noting that Germany, France, Spain, and Italy had a two-century burst of the serial killer phenomenon in the 1600s and 1700s that for whatever reason faded away by and large.