Something like 70% of people have either HSV-1 or HSV-2, I believe. That alone would be unreasonable to manage, assuming you could even wrangle that many people into this imaginary leper colony.

What you're asking is both an ethical and a logistical question.

Yes, you COULD isolate people to eradicate these STDs. But is it ethically/morally correct to do so?

Could you even positively identify 100% of the infected and get them isolated? I don't know that you could. And if you did not, then you are just postponing the eventual outbreak of these diseases further. Possibly worse if people start throwing caution to the wind because they feel safe, and now those infected populations start exploding.