The proposed geared Super Fan was in essence a larger version of the Lycoming engine mentioned by RMM.
Why do you want to use a gear to drive the fan? It would allow the fan and the low pressure turbine to run at their own optimal speeds. The fan would like to run at a speed slower than the turbine. Because of the different optimal speeds, that's why Rolls use three spools for their big engines. But the additional spool adds mechanical complexity. Also the compression system and the turbines are still not running at their respective optimal speeds.
For a given core engine, lower fan speed means it's more feasible to fit a larger fan. This will increase the bypass ratio which means better propulsive efficiency and lower specific fuel consumption. Lower fan speed also means quieter fan. OTOH, a larger fan means more drag and more weight.
Sounds like a good idea, right? Unfortunately, the gear technology necessary for higher thrust engines is not quite there yet. Reliability seems to be one of the major issues.