An earth connection is there in the event a loose (live) wire can manage to make contact with a metal surface which is also in contact with the person using whatever it is. So things like irons, toasters etc are earthed.
These sorts of PSUs don't tend to be, as the mains side is typically partitioned off by plastic dividers within the unit - so there is no possibility of a live wire within the unit breaking free and coming into contact with the DC side - where it could potentially electrocute you through the low voltage cable plug. And of course the outer case is plastic - hence double insulation mark.
You will also note they tend to have anti-tamper screws and no ventilation slots (or shielded slots) so you can't go sticking metal objects in. It also means they can make the earth pin out of plastic (to open the shutters as Adam has said) - which can then break off.
You don't necessarily need to buy an original replacement if you can't easily get hold of one. The likes of Maplin
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do universal replacements (search on "ac/dc regulated power supply")- but make sure you use the correct polarity/type of DC connector from the selection, and the right voltage/current rating. It probably won't say one way or the other on the unit but I'd go for a regulated one for the sake of an extra quid or so. If you're not sure about any of this - just take it all into a Maplin shop and they will help you get the right unit.
It follows that the only time you'd probably find an earth on a radio is if it had an integral mains transformer and a metal outer case.
Midge.