I don't think it would need the whole frame treating, just annealing locally in the area of the welded repair. Cracks in aircraft are welded all the time as part of regular maintenance but the entire aircraft is not re-annealed after.
Each to their own but depending on how bad the damage is, if it was me I would give it a go, if the frame is scrap anyway and out of guarantee then why not. Obviously the frame should be checked regularly for damage but that goes for any frame, repaired or not. At the end of the day the choice is up to the owner of the broken frame, they have to decide if its worth repairing or not and weigh up the chances of any further crack appearing later.