What is the real benefit of doing a like new restore?
I've thought about doing it a few times, but would I lose in app purchases, etc?
No real benefit - not if you weren't experiencing problems to begin with - unless you're about to jailbreak or to do your firmware update. And even then, it might be more of a preference thing. I always do both those things on a "clean" iPhone, but it also works allright on a full device. It's way longer though... hence why I do it from a clean state.
Anything you bought with Apple you won't loose unless Apple stopped signing it. Another way to say this is if it's still on App Store, it's still yours. All you have to do when you setup your iPhone as new is to enter your actual Apple ID for the device. After which, you'll be able to : - force "transfer of your purchases" on iTunes on your PC, or; - reinstall them directly on the device by going into the App Store app in "Updates" and choosing "Purchased" where you will find (most of) the apps you purchased. I guess it works the same with your music on iTunes, but I never tried it, I buy and manage my music directly from my PC. In any case, you should do a complete backup on your PC before resetting your iPhone to new... if something goes wrong or missing, you can always get your things back.