Because it shows how unimportant Omar Little was in the grand scheme of things. He was a drug kingpin on the streets, revered and feared, but after his death he is basically an anonymous body in a morgue and his identity gets switched with somebody who is nothing like him by a non-caring clerk.
This is also shown in other ways:
The news of Omar's passing travels slowly. Bunk is quickly on the scene, communing one last time with the one mope with whom, over the course of these five seasons, he had built an understanding. But Chris and Snoop, for once, are in the dark, dreaming up new plans to catch their foe while he's already on a slab. At the Sun, Gus spikes a possible story (death by shooting of a 34-year-old male) in favour of a few paragraphs on a house fire. McNutty, meanwhile, is more interested in Bunk's other news – a warrant for the arrest of Chris Partlow – and how it might affect Lester's wire.
(It also shows how the system fails at all kinds of points.)