The NHS/JCVI can't sit there thinking only about individual benefits, by comparing vaccine side-effect risks against the risks of illness.
Even if a vaccine is considered as safe as any vaccine can be, and even if the disease would be harmful and well worth avoiding, they're still forced to look at the nationwide costs of deaths and/or hospitalisations it would prevent, to see if it's worth giving out.
If vaccinating everyone doesn't prevent enough deaths and hospital costs, then however catastrophic the illness might be for a few unlucky people, it can't be offered as a free vaccine.
The problem isn't that we have that unavoidable rationing, so much as people not realising that's how it works, and interpreting the NHS not giving a particular vaccine to a particular age group as meaning that age group doesn't need it at all, or even that it's actively not safe for them to have it.
The covid vaccine for middle aged people falls into this category too - so many people think not being offered the vaccine now must mean either that we don't need it (i.e. that covid is totally fine now for middle-aged people), or that the vaccine is riskier than the illness. In reality neither of those things are true, it's just cost (and only short-term costs at that - they don't even take into account the costs of increased rates of cardiovascular disease after covid).
I think we need the government and NHS to be less squeamish about saying "These are the routine childhood vaccinations, but there are others we consider safe but that we can't afford to provide for free". Yes it would lead to pressure to add those to the national programme, but the cat's already out of the bag for meningitis B, so they might as well be honest in general in the future.