The Flashing White light to an aircraft in flight seems completely redundant. They still have to give you the various Green lights for the actual clearance, so the White light hasn't achieved anything useful
It tells the pilot of the aircraft to land at this specific airfield (he may even have his radio on but tuned to a different frequency). This can not be communicated with green lights alone. There may be any number of reasons for that: Maybe the aircraft is trailing smoke. Or the refueller found out that he used jet fuel instead of AVGAS and phoned all airfields in the vicinity. Or the aircraft infringed a military control zone. Whatever.
So whenever you fly in an ICAO member state that has implemented the full set of rules (like the country I live in for example) and you see white lights being flashed at you from a control tower, you better land. It saves them the inconvenience (and you the cost) of scambling the fighters to get you down...