Because you can circumvent the centralized authority of DNS registrars. Look at the Pirate Bay, who keeps having its domain names revoked by central authorities. Namecoin's ledger allows people to agree on who has what domain name without using a standard registrar

But why do you need to sell a name like akqbajauwbzjxu7163jebej? Can't people simply claim names the same way they claim bitcoin wallets?

The goal of Namecoin is to manage meaningful names.

I guess a service that provided free names like the one you made there might be an interesting addition.

In that case I don't get it... do I basically get a random name when I mine a namecoin? And then I try to buy names I actually want from someone who has the name I want? And if no one has the name yet then I have to wait until someone mines it?

I don't know the details, but you do still mine coins into a wallet and all that stuff, there are just special types of transactions where you post a bit of data to the blockchain and that data is the domain name you want registered.