Zero coin and mixers don't provide the same benefit as this.
Using a different address for every transaction increases your privacy. It prevents people that know your address from knowing how much money you are receiving. This technique gives you the same benefit with a single address and also helps prevent fraud.
For example, if Apple sells iPhones for bitcoins and provides a single payment address, then Google can simply monitor that address to know exactly how many iPhones that Apple has sold. So, Apple would instead provides a different address for each transaction, or they use this technique with a single address. Now, Google cannot track their iPhone sales.
Furthermore, one drawback with multiple addresses is that a scammer could surreptitiously replace the address with his and you would never know it. If Apple has a single well-known address, then you know that by using this address you are sending your money to Apple and nobody else.
Exactly. Mixers, zerocoin etc used with this are important parts of a whole and used together help protect your privacy from random hackers and snoops