I think that another factor in the US is the use of a dedicated arrival runway at most busy fields; in such situations arrival spacing is often (not always, though) of little relevance.
EDI is obviously a far quieter field than LHR, but for us visual approaches are a useful tool - they reduce the controller's workload (in my experience) and actually increase our capacity as almost all pilots will fly a tighter pattern than we would have given them under vectors. Under the banner of "reduced separation in the vicinity of the aerodrome" we would routinely clear the first two in a sequence for visual approaches (always in response to a pilot request). Mis-ident of traffic ahead by crews is (again, in my limited experience) not a factor. I can remember it happening once, but (in fairness to the crews) the controller made a very poor call on that occasion.