"Could HIV be eradicated by merely halting all transmission?"

Yes.

Given that this virus has already made the species shift four times that we know of, "halting all transmission" is sort of a strange concept.

Yes, but that would require an effort by an organisation like WHO of a scale never seen before. I would be very proud of the human species if we could pull this off.

I think, as a species, we'll master time-travel before consensus...

Smallpox was a plague of similar proportions, and the world community got together and pulled the massive feat of erradication in a decade.

It's not like HIV.