In the UK the radar controller is responsible for separation on final approach and if two a/c became 1.5nm apart the radar controller would take action to separate them. 1.5nm between two jets is a non-landing situation for the second unless there was a very strong surface wind and you had some fast turn-offs. Remember that as an ATCO you are there to ensure safety; you can't simply let an aircraft continue in a dangerous situation simply because #2 has #1 in sight.