Karl, the folks who have never experienced a catastrophic failure of a high speed assembly like a flywheel or a clutch may be of the opinion "no biggie, weld, glue or snap off the opposite fin".
Those who have experienced or witnessed such failures will be understandably steadfast to the philosophy of "replaced it at all costs."
There is also middle ground that has been expressed here too. Have the part taken to a machine shop, checked for cracks and have the broken fin and the opposite fin MACHINED off (not broken off) and a quick check of static or even dynamic balance and you have a useable flywheel, You will be paying out $$$ for this precision work.
I agree with the replacement philosophy and the safety factor that affords you and your family. You would probably never think of pointing the outlet of your mower toward your family while your mower is running over a gravel driveway - please don't think that a flywheel exploding would be any less a danger to your family or friends.
The key here is understanding. Understanding (and sometimes experience with) the forces involved in a chunk of cast iron leaving the engine area at speeds well over 100mph. Also, check out Google or YouTube for a brief introduction to the MagnaFlux process. Once you understand how a small crack in cast iron (most often undetectable by the naked human eye) can ruin your day, you will also understand what must be done.
Live long and prosper.