Fellas! Please look at a motor torque-speed characteristic curve. In North America that would usually be a NEMA Design B curve. Note that the starting (locked rotor) torque on these typical motors is about 160% of full load. That's the starting torque that you will get with a magnetic starter. Note also that the current required to get that torque is between six and eight times FLA.
Now note on the same torque-speed curve the breakdown torque which is the peak torque the motor can deliver. It occurs just as the motor is overloaded to the point that it becomes magnetically dis-synchronous. Note that the torque at that point is 220% and the current required to get this torque is around 240%.
The beauty of a properly engineered drive/motor system is that you can start right at that peak current instead of at the (usually) lower locked rotor current. In the case of the NEMA Design B motor, that's an increase of 60%. And you can do this with a drop of current from 600% to only 240% of nameplate.
Now, the key to this is the "properly engineered" part. A drive with the same hp rating as the motor will not do this, not the heavy-duty version nor the normal duty version. You have to size the drive to provide the required AMPS, not HP. When this is done, you can actually start with 60% more starting torque than across-the-line.
The examples cited above where the VFD-driven motor didn't have the torque to start the load are simply examples of improperly designed systems. I'm not trying to trash anybody's work here but simply trying to give you the facts so this kind of trouble can be avoided in the future.
As to the comment about all motors on VFD's being "inverter duty", the problem is that the term "inverter duty" means different things to each different motor manufacturer. What is clear to me is that all motors on VFD's running 400VAC and higher need to be insulation class F minimum. Yes, that's all motors. Further, while many are not and get away with it, all motors on inverters running 400VAC and higher should also be MG1 Part 31 endorsed or equivalent. Yes, that's all motors too. Beyond this, the application has a large impact on motor selection. If you are dealing with a centrifugal pump or fan with a speed range of 4/1, an Open Drip or TEFC motor is plenty good enough as long as it is Insulation Class F and MG1 Part 31 rated. On the other hand, if you are dealing with a constant torque load like a conveyor, auger, or many industrial machines where the full torque speed range takes the motor below 20hz or so, you need to deal with the motor thermal issues at slow speeds and heavy loads. You may need to chose a TENV motor if under 30hp or an auxiliary cooled motor if larger than that.
Finally, leitmotif, did I make myself clear about the available starting torque when the gear ratio is increased? If not, let me know and I'll try again using some specific numbers.