Stuff happens in real life. You try to start the motor and find out that the bearing lube oil pressure switch is faulty and trips out after running for 3 seconds. Or the vibration switch on the fan was set too low and tripped durign acceleration. Then it happens again. Do you wait an hour or do you make the quick repair and restart the motor?
Some applications have the motor starting several times a minute or more on a machine. Those motors will be designed for it.
The Hot/Cold start criteria you are referring to is a standard to prevent "standard" motors from burning up due to frequent starts. Every time a motor starts it draws 4- 12 times its full load current to accelerate itself and the load up to speed. Since heating due to current is = current squared x resistance, the heat in the motor during acceleration can be 16 to 144 times normal or more. (I'm ignoring the rotor heating which is also very important.) If you start the motor too many times without giving it time to cool down, it will fail either by an insulation failure or the joints in the rotor melt loose.
Standard motors are designed to be able to accelerate their rated load to full speed twice if they start ouy cold but only once an hour if the motor was already at operating temperature.
This is usually only applicable to large motors >100HP, but can apply to smaller units.
You could have gotten this information by looking at any of the many motor manufacturers? web sites. Most have excellent tutorials. Take a look for better explanations than mine.