This style outlawed any submissions or grips below the waist, making the grappling exclusively upper body. It has a very specific rule set, which works as a strength for the practitioners.
1) Greco-Roman wrestlers are very strong in the clinch. Unlike Judo, the jacketless grappling of the Greco-Roman style transfers over to MMA clinch fighting very well.
2) The extensive use of underhooks, overhooks is central to success in Greco-Roman style. It gives the wrestlers a good vocabulary for MMA fighting.
3) From the clinch, the style has a good number of takedowns, throws and suplexes which can be used very effectively.
4) The first few pioneers in the sport came up with techniques to strike while in the clinch, and also found ways to land strikes while exiting the clinch. They called it dirty boxing, and it transferred well into the cage.
5) Fighters like Randy Couture, Dan Henderson and Matt Lindland came up with techniques to use the cage to prevent and aid with takedowns. Greco-Roman wrestlers are adept at pinning and controlling their opponents on the ground.
Greco-Roman wrestling does provide a strong grounding in certain aspects of the skillset required for mixed martial arts, it needs a good deal of additional skills to be made into a strong MMA base. But when those additional skills are added, it can come together to result in a very strong fighter.