Does a compressor with a short to ground really require a complete system replacement?
The compressor is the "engine" of the AC system.  It, and a few valves, and the condenser fan, comprise all the active portions.  Everything else is passive.    The compressor is an electrical motor connected to a precision pump.  The pump has to be lubricated by sufficient refrigerant (Freon or substitutes).  If a compressor seizes, it may burn out the electrical motor, causing the electrical windings to short out.

Long story short, a failed compressor may be a reason for system replacement.  You would be well advised to get a second opinion from another contractor.  Get quotes for both repair and replacement.

Another reason to replace the system, is the mandated phase-out of R22 refrigerant.  If your system is older than 5 years, it probably uses R22.  While an existing unit doesn't need to be replaced, per se, because of the phase out, practically, it will, due to the price of the refrigerant.  I just paid $5/ounce for my system recharge.