Yes, this transaction style can achieve some similar outcomes but it doesn't require computationally expensive / difficult to trust novel cryptography, and it doesn't require changing the Bitcoin network nor does it require an altchain. Not does it require a trusted initiator. And it should have much better scalability for small mixing groups.

On the flip side, making it into something useful to many people still requires a lot of development, and potentially a little bit of novel cryptography (e.g. even zerocoin itself) to prevent denial of service... but that stuff would be external to Bitcoin— just software the users need to worry about, not everyone. And it would handle large anonymity sets poorly, the practical limit is probably on the order of a hundred or so parties in a transaction... though funds could go through multiple levels of common sending.

I personally think joint transactions a much more realistic technology for improving Bitcoin privacy and preserving Bitcoin fungiblity than Zerocoin is, at this time.  Though zerocoin certainly is more crypto-mathematically exciting.  Though I suspect that people's lack of interest in techniques like this (note the date on the original post) suggests that people don't really consider the privacy/fungiblity problems as bad as the hype around ZC suggests they do.  Maybe if I'd given the thread a snazzy name like "INVISIBLE HAND" people would be more excited.