The "assuming it could be done" in my comment referred to "finding a way to force latent cells to release their viral load rather than remaining latent". I'm not an immunologist, but if there was a mechanism, it would probably kill the rewritten cells. Then the released viruses would be eliminated with anti-retrovirals.

If this same mechanism kept infected cells from remaining latent, eventually you would clear the virus.

So I don't know the answer to your question, but my answer was assuming an answer existed :)

Several things come to mind. First, you don’t need to remove viral DNA from cells. Just make them over-express HIV and trigger cytotoxic lymphocytes or antibody-mediated killing. You end up wiping all the infected cells. But then, of course, patient is left with compromised immunity. To solve this, you could make a stem cell transplant from a compatible donor. Alternatively, harvest healthy cells before the treatment and transplant them back after.

This is from the top of my had, I’m not an expert in the field.