Good lord, I would never, ever have contemplated the thought of welding a flywheel. That is based simply on intuition. Many things can and should be welded, (I just had a fair amount of welding done on my K frame, including the perch that holds the motor mount in place), but there are things that to me should not be repaired or welded. A flywheel is one of them.

Heating metal to welding point does change the crystalline structure of the material, to whatever degree. In some cases it is negotiable, in others not so. So essentially you now have a spinning object with considerable centripetal force and differing, uneven crystalline structure throughout, directly perpendicular to your feet and lower legs.

That is not based on any scientific investigation or knowledge on my part, but unless convinced otherwise, that is something i would never do!