Are all of the servos always driving, or are there situations where at least one is back driving and generating back to the power supply? If the friction is low, and inertia and acceleration are high, then you will have times when some motors are drawing power and others are generating power. This is a common situation in machines with servo motors.
If this is the case, then your power supply must handle two extreme cases:
1) The maximum number of motors are drawing the maximum amount of power.
2) The maximum number of motors are decelerating at their maximum rate. A typical case is when a fast stop of all axes is commanded.
Note that a motor with a reasonably efficient drive drawing 5 amps at six volts will pull 2.5 amps from a 12 volt supply.
Industrial servo drives with significant amounts of regenerated power and multiple motors will use a common DC buss. A single battery powering all motors counts as a common DC buss. A battery capable of powering all of the motors will absorb all of the regenerated power. So, yes, a car battery should make a good power supply. Be sure to check the drive specifications to make sure that they are designed for 12 volt input.
This assumes that you have four quadrant drives that can regenerate back to the power supply. Some drives just dissipate regenerated power into a resistor, in which case there is no power regenerated back to the power supply.