The main reason transmitters are banned on aircraft is not _known_ problems. Rather it is that they can't be sure there won't be problems. Even if they tested a dozen cell phone models... what about all the others.
An accurate description, but there is more to it than that. If there are several cellphones in operation then the transmitters mix with each other and with the aircraft's own radios to produce many new frequencies. These intermodulation products increase exponentially with the number of transmitters and it is virtually impossible to predict every possible combination.
Using an on-board base station, not only is the power of the phone transmitters restricted but the range of available frequencies can be limited to ones that have been calculated and tested to ensure compatibility with the aircraft equipment.