If your motor is built to MG-1, I believe the standard is that it will start successfully at 90% voltage, provided load inertia meet values complying with those given in MG-1. MG-1 also states that for lower starting voltages, the speed-torque curves must be evaluated to determine if starting will be successful.
Starting at much lower voltages is obviously possible, since reduced-voltage starting is commonly used. It just depends on your driven equipment.
So, to answer your last question, if motor load meets MG-1, and the motor failed to successfully start at something less than 90% voltage, then the motor manufacturer would probably tell you the problem was with your system.
Please bear in mind that the 90% voltage is based on the motor nameplate voltage which is generally less than the system nominal voltage to start with. So the situation may not be as bad as you think.
For large motors, it is a good idea to provide a minimum starting voltage in the specifications. If you purchase the motor with the driven equipment, you can place some of the responsibility on the supplier to provide a system that will successfully start at whatever voltage you specify.
Hope that helps.