I'm not sure how that would help? If you had a flywheel and you didn't need the energy, what do you do with it? At least without a flywheel, you can easily stop the turbine.
Also, any flywheel that would add significant difference would probably weigh hundreds of tonnes, which would make construction massively more expensive and difficult.
If you don't need the energy you just let the flywheel spin freely. It's a mechanical battery. I agree with your second point though- it would add considerable mass to the hub assembly of the wind turbine and there is no clear way to transmit the mechanical energy to ground level.
Also, any flywheel that would add significant difference would probably weigh hundreds of tonnes, which would make construction massively more expensive and difficult.