I know that earth has a very high capacitance (of about 711$\mu$F) and it would take a lot of time for this but since we earth almost all our appliances for safety, wouldnt one day come when earth doesnt have the ability to store more charge and therefore we cannot earth our appliances? And even if it does, what would happen after that?
Maybe this will help:
A key thing to bear in mind when using this formula is that Q refers to the charge separation of the system. In other words, when I say that a capacitor is charged up to some level Q, I mean that I have put +Q on one part of the capacitor,-Q on the other. The capacitor as a whole remains neutral!! I emphasize this now because I often find students are somewhat confused by this point, particularly when we start thinking about circuits that have capacitors in them.
It then depends on what is the +Q or the -Q in our circuit with respect to the earth, it is not a fixed nor a conserved amount. It is not something that can be saturated.
Read 6.2.1 for the earth as a spherical capacitor.
The capacitance of the earth is so large that one can effectively remove charge or add charge without changing measurably the potential.
Now if one starts thinking of the basic carriers of charge, electrons and ions, in total the earth is neutral, and it is potential differences that define the separation and motion of charges, and conductivity on how fast charges are diffused.
Earthing will not be used up and cease to be an option. Safety earthing does not rely on the planet's capacitance or conductance.
Electrical power systems move charge only in the same way that the fixed engine of a cable-car system moves metal wire. There's no net accumulation of wire at any single point. The cable car system doesn't eventually run out of places to store the wire, it gets recirculated continuously.
Safety earthing (also known as grounding) is largely a local arrangement that does not make use of the planet's capacitance or conductance.
In a home, all the metal pipework and the "earth" wire of fixed power wiring are all joined together at a common point near where the electrical supply first enters the building. It is primarily this that provides the safety.
The idea is that if a live-wire accidentally contacts a copper pipe (for example), a large "short circuit" current will flow because the pipe is connected to "earth" - and this will cause an overcurrent protective device (fuse, circuit breaker, etc) to isolate the live side of the circuit and make it safe.
There are also residual current detectors (RCD, GFCI etc) which look for imbalances in current between "live" and "neutral" conductors - and isolate circuits where an imbalance suggests an unsafe leakage through another path. I believe these are used in two main circumstances:
where you need the safety system to isolate the live current faster (or for smaller currents) than a fuse or circuit breaker can react - e.g. electric lawnmower cutting its own cable with its wet metal blade while a human is holding its wet metal handle.
in homes whose internal power cables lack a protective earth conductor (e.g. many US homes of older construction).
In some countries, this home "ground" point is also usually connected to the "neutral" wire of the household power cabling.
In some countries, this ground point is actually connected to a local "ground rod" or stake driven into the ground. But elsewhere this is instead connected to a "protective earth" or combined earth-neutral power wire in the electrical supply cable.
See Earthing systems