Hopefully this answer isn't redundant.
Astronomy is done over huge orders of magnitude. To make things manageable, we try to keep numbers under a thousand - it's both more practical and more intuitive. This is reason #1.
The second reason why we don't set our zero point to the beginning of the Earth is because it's a measured quantity with an error. If you set your clocks to the 'beginning' of the Earth (which by the way is not a well-defined statement since the time of the formation of the Earth is actually an inclusive range of times), you would have to report the year as:
$$ 4,540,002,013 pm 50,000 text{ years} $$
Though the zero-point is certainly arbitrary, it at least defines a point in time where we can use clocks to measure from.
Lastly, why do you think the age of the Earth is the relevant zero-point? Why not use the beginning of the Universe?
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