Characteristics of Ferrite cores
It is possible to make a ferrite transformer for response down to 50Hz .However there is a penalty .Garden variety ferrites are only good for around 300mT where the more orthodox laminated iron core is good for at least 1 Tesla .Your proposed 50Hz ferrite transformer would have to have about 3 times as many turns if it was to be wound on a core of the same area as the standard laminated iron cored transformer.So copper losses would be up and power rating would be down and voltage regulation would be worse .If you want to keep the winding DCR the same and hence not lose anything the proposed     ferrite cored transformer would be much larger .Ferrite cores were used for telco Audio where I had to get down to 300Hz in a Napier branch of a Swedish Telco company .The power was very low like I think +6dBm so the size was not in the day an issue .RM8 cores were used as a mainstay and I sometimes used high pearmeability RM6 .The upper frequency response of these was superb but we limited things to 3.4 KHz .It would be interesting to try a ferrite output transformer in a valve amp where size does not matter .