A third purpose for an interwinding screen - on appliances that have a mains earth connection - is safety.
In the event of the high voltage primary insulation breaking down - perhaps through over-temperature if the supply is heavily loaded - the interwinding screen will short the primary side to earth, thus protecting the secondary side (and you!) from dangerous voltages, and causing fuses or breakers to disconnect the supply.
This obviously does not apply to "double insulated" devices with 2-pin mains connectors and plastic enclosures, which are protected in different ways.
But a desktop PC power supply (with metal case and earth connection) this is an important part of the safety system.