Barrel length is the only reason why the original USGI and many commercial models are restricted. The 18.5 inch minimum barrel length for centerfire semis came in during the Turdeau years, with one of the main reasons being to discourage widespread ownership of the M1 carbine.
As far as NR models go, the new Auto Ordnance carbines being sold at many dealers are over the minimum barrel length, and there are some older commercial models that had long enough barrels as well. Also, many people used to either have their restricted carbines (USGI or some commercial) re-barreled or have extensions permanently attached to the end of the barrel, in order to make them non-restricted. In the case of the former, it will make it NR, but in the case of the latter, it is no longer accepted as counting toward barrel length, so that is something you may need to be aware of if you happen to come across one done like that which the owner may think is NR.