The problem with 'just' welding the frame is that where it cracks is a weak point, and any weld will always introduce another weakness due to the heat stresses.
If you look at the frames that come as replacements (900FE usually) they have a different gusset in the area that cracks.
If you then have an accident that can be attributed to the frame breaking, it will be your problem not ducati's.
Technically, you may also have to tell your insurer's you have a modified bike
My bro-in-law also (fairly recently) had a replacement.
I'm sure he'll be along soon.
Welcome to the board by the way, and thank you for asking, I'll have another ice-cold v-guinness.