I'm not talking about research, I'm talking about public health and mandatory for school vaccinations. Surely you're not claiming that children are being involved in a secret research project starting at 15 months of age?!?
Considering that the vaccine hasn't been available for 20 years yet, there aren't a lot of health care workers whose immunity derives from the vaccine yet unless you count candy stripers and even there, it's not 100% of them since the vaccine wasn't mandatory when it came out.
I agree that learning how the immune system forgets would be extremely valuable, but that isn't anywhere near on-topic here and certainly doesn't count as a justification for the Varicella vaccine for school children.
It may be that data derived from tracking vaccine performance would be helpful, but the value is likely limited WRT autoimmune since in the latter, the immune system will be constantly stimulated.
The data point on breakthrough cases is more an observation that having chicken pox is 100% effective at immunization (with the exception of immune compromise where vaccines don't work either).