I don't think there is such a thing as broken beyond repair. How would you even begin defining that? If you're thinking in economic terms then sure, we can try to optimize a limited budget to save/improve the maximum number of lives. It would still be beneficial to have at least a few people look into whether new methods can be developed to increase the amount of "good life" you get per dollar. Giving up and deciding something is beyond repair can be one course of action in this optimization, but it seems counter productive, and perhaps a bit unethical, to try and generalize this position. Having the thought, and the discussion, is obviously totally fine.
A burnt match is broken beyond repair. And certainly there are human medical conditions which presently elude our technical ability to "repair" them. Rabies is a good example; if we didn't have the vaccine for it, then I think it would be pretty clear that an infected person is broken beyond repair.
