@StarUtopia
There are well founded public health reasons for not vaccinating against chickenpox that do not apply to measles.
Chickenpox can absolutely be a serious illness and may cause death. However, the risk of disability or death as a result of chickenpox infection are lower than for measles. And, where serious complications do occur they often result from 2ndary bacterial infection - for which there are antibiotics. The chickenpox virus itself can be attenuated by aciclovir. There is no treatment for measles other than IVIG.
I don't think that the chickenpox vaccine has as higher rate of lasting immunity as the measles vaccine. So one concern re introducing a chickenpox vaccine, particularly if uptake wasn't very good, is that as a consequence a higher number of people would acquire chickenpox later in life. Chickenpox is much more dangerous later in life. At the moment, it is so prevalent that almost everyone is exposed during childhood - and hardly anyone is left to be exposed as an adult. But if 70% were immunised, then the remaining 30% would "miss out" on childhood chickenpox and have a much higher likelihood of the more severe chickenpox infection of adulthood. Even if nearly everyone was immunised, if the immunisation doesn't last forever, the same would hold true.
Whereas measles is the most dangerous in immunocompromised people but otherwise is not more dangerous in adolesence/adulthood than it is in childhood. In fact, the most ghastly complication of measles (SSPE) is more likely, the younger you are when you acquire the illness.
Lastly, exposure to children with chickenpox attenuates and reduces the frequency of shingles outbreaks in previously infected adults. So if we immediately reduces the number of childhood chickenpox cases, then shingles would go up. Shingles is also miserable and sometimes dangerous (can threaten sight if it occurs in the ophthalmic branch of the trigeminal nerve).
The NHS did produce an information sheet on why chickenpox immunisation isn't currently on the schedule - think it can be found online. Obviously, if certain health or demographic factors changed, then the recommendation might change.
And for some people, immunisation against chickenpox certainly is worth pursuing - I would suggest that a person who has reached adolescence without acquiring chickenpox should seek immunisation.
Please anyone correct any errors, as I'm just going on what I can recall.