For the most part, neurons do not replicate or they replicate infrequently. I'm not sure where you come up with the statement:
"Killing infected latent cells is not going to cause neurological issues if it's a very small % of cells"
Can you cite me a study that says a very small percentage of cells are infected, and killing them (i.e. the infected neurons in the Dorsal or Trigeminal ganglia) is OK?
Regarding studies where they have removed the virus from a living latent cell, here you go:
Please watch the ENTIRE video. Also, pay close attention at 6:44 of the video
I don't think that's what happens. I think that normally the reactivation of HSV in neurons is so short and it emits a small number of viral particles that it is not detected by the immune system. It is similar to what happens with HPV copies in the deep dermal layer. Latency and very short activity is a mechanism of survival of viruses.