The undesirable qualities of bipolars are base current, low input impedance, and thermal runaway due to both inherent heat properties of silicon and the phenomenon called the Early effect (AKA base width modulation) and base current recombination. The input capacitances (Miller and shunt capacitances) are also there and variable due to the aforementioned Early effect.
The bipolar transistor's input is now more controlled by the signal than would be previously realized. This is because the output of the source of the FET is now in phase. That is, the voltage signal and the current signal are in phase. This is significant when one notices that if the voltage and current were not in phase, say by 180 degrees, then as the signal voltage went positive, the base current would also go positive, because the bipolar is now conducting more, but the base current will be out of phase with the signal current, so cancellation will be the result.