You asked: Will shredding documents that only have my name and address details on them protect me against identity theft, or offer any other information security benefit? The bigger question which cannot be truly answered is: "If in the event of identity theft, was it due to you not shredding documents?"
Most of the times when it's time for me to dispose of personal documents, I have not gone as far as shredding, but instead either ripping out that portion of data (names, account #'s, etc) ripping that into little pieces, and disposing of it in entirely different trash bags/bins.
When it comes to dumpster diving, this has mainly been an issue of attackers targeting companies moreso than individuals, however many private investigators do perform dumpster diving, and I am sure there are individuals with malicious intent, doing the same thing. The initial question is: "What can someone do with this information!?" A lot.
Consider the American Postal System. There is a form one can fill out to notify the postman that they have moved to another address. The USPS usually begins sending mail to this location after about 10 days. This is a blessing when one is moving, but a curse to ALL AMERICANS. Fact: If you submit the form in person, you need to show ID (Good). Fact: If you fill out the form and mail it in, the USPS automatically starts forwarding your mail without validating you requested the change of address. (Try it if you'd like, complete a change of address to say your parents home, and mail it)
So, as an attacker, if I targeted you, I don't necessarily need to dumpster dive. Why would I when I can forward all of your mail. Imagine doing something like this to coincide with the last week, and first week of the month (usually when bills arrive). I'd receive your mail, to which I can gather data to escalate an attack without ever touching your garbage can.
There are other methods to obtain your data, it all depends on the skill of the person targeting you, and the level of data they want to get, and why. Think about it, you would have to be targeted for someone to pull this off otherwise, if I am random attacker going this route (dumpster diving), I am going to target big money. Dumpster diving in Alpine NJ, or Beverly Hills.