And while it's possible there may be no cure, that can also be said about many illnesses - the response to an incurable illness isn't necessarily to kill your patient.
If indeed it could be called an illness, it is not the same in scope as any illness that has ever existed. It's an affliction that's gone global and that threatens to make humanity extinct.
You can't really compare the barn to a mental hospital because even those in there can still reason, speak, and aren't constantly trying to eat other people unaffected by their "disease". And even if they were trying to, if they greatly outnumbered the sane population, you can bet that some killing would happen.
The morals will change to fit the situation, and Herschel just never figured that out.