Why not?
Now asking An Post to overhaul their system to work on postcodes only is a bit like asking a postal service which requires postcodes to make them optional. It's technically possible, sure, but they're not going to want to spend the money.
_That said_, An Post's last resort routing department is pretty famous for getting the right address from pretty fragmentary information like "Mary down by the church, formerly of Kilnowhere", so I'm sure if a letter with just a eircode arrived there they'd sort it, but I imagine that An Post don't want to encourage people doing things that increases load on the labour intensive sorting.
<Moist ran downstairs and Lord Vetinari was indeed sitting in the Blind Letter Office with his boots on a desk, a sheaf of letters in his hand and a smile on his face.
'Ah, Lipwig,' he said, waving the grubby envelopes. 'Wonderful stuff! Better than the crossword! I like this one: "Duzbuns Hopsit pfarmerrsc". I've put the correct address underneath.' He passed the letter over to Moist.
He had written: K. Whistler, Baker, 3 Pigsty Hill.
'There are three bakeries in the city that could be said to be opposite a pharmacy,' said Vetinari, 'but Whistler does those rather good curly buns that regrettably look as though a dog has just done his business on your plate and somehow managed to add a blob of icing.'>