that loud noise is called “ringing”. On industrial grade VFDs, you can eliminate that sound by changing the carrier frequency setting.
As far as motors that are designed for VFD use, they are called “inverter duty” and the difference is in the insulation used. Class “I“ insulation is made to withstand the heat that causes lesser insulation to break down. Inverter duty motors are more expensive, and I would argue an unnecessary expense for a grinder. The killer of motors is heat. Running a motor below half speed for a very long time cooks the insulation because the internal fan is not moving much air to cool the windings. That’s what class I insulation is for. It will take a lot more heat before it begins to break down. But we typically aren’t running slow all day long. If you are, then an inverter duty motor is a good idea. For most of us, it’s good practice to touch the motor after a while. If you can lay your hand on it you’re fine. If not, turn the speed up and take a break while the motor cools itself.
The biggest downfall of electric motors today is that the small HP stuff has all gone to rolled aluminum frames. They are disposable and meant to be. Industrial companies don’t rewind small HP motors because it’s cheaper to throw them away and put another on. 5 minutes and the production line is running again.
Can you get a good quality motor under 5 HP? Sure. Leeson, Baldor, etc are good motors. But few of us will run a motor hard enough on a grinder to ever know the difference.