Vaccines for herpesviruses are not easy to make because the virus can evade the immune system by laying dormant in nerves, among other things. It's just a tough family of viruses to pin down. There's a phase 1 EBV vaccine [1] but it'll be a while before we see progress.

[1]: https://www.nih.gov/news-events/news-releases/nih-launches-c...

> If the downsides outweigh the upsides, why aren't we just eliminating them, as we have done for more deadly viruses like smallpox and polio?

- We don't have an effective vaccine yet, let alone one that is sterilizing.

- More than half of the population has HSV-1.

- HSV-1 lies dormant then reactivates and sheds, often asymptomatically.

It's unclear how you'd eradicate it, given these facts.

I'm unaware of ANY viral infections having any upsides, possibly excepting whatever's native to our gut microbiome. And herpesviruses are very complicated to fight against.

Eliminate them how? They're largely asymptomatic and hide from our immune systems in various ways.