Mr. Laser Beam wrote:
And if he had used his blood to treat her, it might have caused her body to expel or kill the eel as a foreign substance.
There is no reason to assume that. Kirk had suffered from fatal radiation damage, which is damage on a genetic and molecular level, disrupting cell function and replication so the body's cells can't be repaired or replaced. Lucille Harewood had an unspecified terminal condition, which may well have been genetic or involved failures on the cellular level. We don't know what killed the tribble, but if it died of old age, say, that's a cellular/genetic/molecular process as well. And of course Khan is genetically augmented, his abilities due to changes in his genes and probably the associated epigenetic mechanisms. This might include an enhanced ability for genetic and cellular repair. So it stands to reason that Khan's blood would be effective at healing genetic or molecular-level damage.
But what you're talking about, expelling a parasite, is an immune reaction, not a repair mechanism. It's a totally different biological process, like the difference between driving off an invading army and rebuilding the city they trashed. So there's no reason to assume Khan's blood could function as a super-immune system as well as a super-repair system. It doesn't follow that it could drive out a parasite.