Generally why are one of the two plates of a capacitor earthed?
if it is grounded, it is because the capacitor housing is either directly connected to this grounded plate, or very weakly insulated from the voltage. this is done for security and can only be implemented in certain types of circuits.
The premise of the question is wrong. While a terminal of a capacitor may be grounded for some applications, such as smoothing the output of a rectifier bridge in a power supply, there are many applications where no terminal is grounded . for example, as a decoupling capacitor.
Capacitors are used in a wide range of circuit configurations.
as coupling capacitors in amplifiers, in synchronization circuits cr, in multivibrators or by coupling grids of thyristor phase control systems, in continuous blocking for instruments, for starting single-phase motors, washing machines), in protection networks (suppressors) through relay contacts, etc., none of these solutions would work with a grounded side.
Many capacitors are used in parallel with DC power supplies, tank capacitors or local decoupling. these necessarily have one end connected to each power rail and you will often find one connected to the ground. it is a system design decision, and the grounding of one side of some capacitors is fortuitous. This is no longer to do with capacitors.
Then there are elaborate capacitors used on high voltage power distribution, for harmonic filtering or power factor correction. one side of these is usually grounded. but again, it’s not because they are capacitors, it’s because it’s the circuit configuration required to achieve the desired function. (These capacitors, subject to enormous strain, are carefully designed with the outer plate as part of the grounding, because of the way they will be used.)