I think it is more for the customers on the train
This style of announcement dates back many years to the era of compartment trains, slam doors, and trains without public address equipment. It was designed so that people onboard the train could hear where they were at. I suspect, like many other things, it is still used nowadays "because it always has been". When each new Public Address system was installed over the years many of the scripts were just copied from one system to another, so the same style of announcement continues.
If you watch the British Transport Films production "This is York" from the mid 1950s, you will hear the manual station announcer announcing trains in the station. All her announcements generally begin "This is York. This is York. The train now at Platform 8 is the ......". Many of them also begin with the wonderful "Train Announcer Calling..." before the rest of the announcement. Some other wonderful announcements on that film are "Train Announcer Calling. May we remind you, have you left anything in the train? Have you left anything in the train?" and the fact that the times are all in 12 hour clock and no zeros are announced, for example the "0802 train" is announced as the "Eight Two train". Even better is the chance you get to see her. Lovely lady with her pearls and best Sunday dress on talking into a wonderful old microphone with the best Queen's English pronunciation!
In recent years a particularly obscure announcement was the Phil Sayer announcement heard across the SWT network the other year - "On behalf of all the train operating companies, may I take this opportunity to wish a very merry Christmas and prosperous new year".
A System BR installed on some West Coast stations and lasted until about 2008 at Wigan North Western and Warrington Bank Quay used to end the "Train now standing at Platform x is the xxx" announcements with a pause, and then say "Good Morning / Afternoon / Evening, welcome to Wigan North Western".
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As far as I know they are announced once when the platform is allocated, and once five minutes prior to departure (featuring the infamous "Will passengers intending to travel on this service please join the train now as it is ready to leave" phrase).
At Manchester Piccadilly these announcements cause Chaos when they stack more than one train on the same platform. There can be two, sometimes 3 trains already there, if they are Northern ones often without the door locked. The train coming in triggers the announcement "Platform 2 for the xxxx First Transpennine Express service to xxxxx. Please travel in the front train only for xxxx xxxxx xxxxx xxxxx. platform 2 for the ....". Now of course when this is announced the TPE train isn't there, so the unsuspecting get on the open Northern unit - as that is the front train!
The use of track circuits for announcements etc is always on dodgy ground. At Keighley the new wonderful system they installed the other year always shows and announces every single train going towards Leeds and Bradford as being 3 minutes late even though they are invariably on time. At Hebden Bridge in an Absolute Block signalling area the "The Train now approaching Platform 2 ...." announcment is about 6 - 8 minutes before the train, which every so often leads to the wrong train being announced.