There are two important limitations: 

First, the high withstanding voltage required of the capacitor, along with the high-capacitance required for a given output current, mean that this type of supply is only practical for low-power applications. (The capacitance needed increases with the current to be drawn; high capacitance mains-voltage capacitors are expensive and bulky.) 

The second is that due to the absence of electrical isolation between input and output, anything connected to the power supply must be reliably insulated so that it is not possible for a person to come into electrical contact with it.[1][2] By the equation of state for capacitance, where {\displaystyle I_{c}=C{\frac {\mathrm {d} V}{\mathrm {d} t}}}, the current is limited to: 1 amp, per farad, per volt-rms, per radian (of phase). Or {\displaystyle 2\pi } amps, per farad, per volt-rms, per hertz.