I remember an early passage from Buckminster Fuller's Grunch of Giants where he tells the reader to visualize fully packed stadium and explains that's what 10,000 people looks like.
However,a second major issue is what’s mentioned in the movie, that the viral genome integrates into the host genome and can lie dormant for years. So even if you kill off every single viral particle, years later new particles can be produced from the dormant genome.
A third major issue is that HIV specifically infects T cells, which are the very immune cells that are supposed to combat infection. This weakens the natural defenses, and also makes it difficult to create a successful vaccine.
even when medicated -- for decades -- viral particles hang out safely in the body, often in the lymph nodes. as soon as the medication stops, they bounce back.