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The NZAIP states, under the heading Position reporting during instrument approach at a controlled aerodrome, that a pilot MUST (among other things) report "when the ground or water becomes continuously visible and flight by reference to instruments is no longer required.
I would imagine that most, if not all, other countries have the same requirement in their publications.
Oh yes, rest assured that the air traffic controller does want to know when you are visual. It is helpful to know the actual flight conditions that the pilot is experiencing - remember the approach radar controller is probably sitting in a dark room, possibly many hundreds of miles away from the aerodrome (as is the case in NZ).
In in order to enable the controller to expedite the traffic flow the pilot has to voluntarily "Request Visual Approach". The controller needs to hear those 'magic' words before he can issue a "Cleared Visual Approach" instruction. A controller is not permitted to badger the words from the pilot.