What can be the cause of insulation failure inside a 630Amps MCC cubicle?

Improper or No Preventive Maintenance.

Loose Connections

It is less likely but face in Old MCC Insulation failure due to Condensation by High Air conditioner Cooling set points.

630 Amps is a lot of current which is enough to cause death. The conditions you are specifying suggest excessive heat generated within the mccb which melted the plastic enclosure/insulation and probably shorted the contacts. This can be caused due to the following :-

1. Overloading the mccb

2. Inappropriate motor starter or under-specified mccb

3. Excessive load on the motor or jammed/broken motor bearings

4. Loose contact at connection terminals

5. Though unlikely but inadequate ventilation of of mccb during startup of motor might also be the reason

6. Lack of regular maintenance and checkup

7. Contacts erode with time, maybe the mccb is too old to be used at its specified rating

The most likely cause as per the condition specified is either shorting of phases or loose connection at connection terminal as this causes flashes. Overloading will not cause flash unless shorting or loose connection occurs. Also be informed that when overloaded, any metallic circuit element (wires, connectors, bus) may heat up due to lack of conductivity for the current passing through it. It will just act as a electric heater and might turn red hot which can also cause damage and ignite flammable materials.