The original establishment of National Insurance was to cover the 3 areas. General taxation may well supplement this and NI may well be used as a more general tax but it does not detract from the fat of NI, its purpose and therefore our entitlement to all defined benefits
The entitlement comes from policy, not from having paid NI. It's a hard discussion to have because everyone seems to think it is a sort of sinking fund. In theory NI could be abolished and it really wouldn't matter with regard to its funding. It isn't specific to that flow of funding.
Yep. For example, JSA is tied to the fact of one having paid NI but free at the point healthcare isn't. Nothing of that is "logical" or "unchangeable" in principle, it's just the policy controlled by the Parliament.
JSA is monitored from being in the taxation system, but is isn't paid or 'funded' by NI.
Ah, of course - if this is what is being discussed. There is no money earmarked for that from a specific tax (NI). But there is at least an arbitrary link between the two (also set by legislation), which is missing for other services. Entitlement indeed doesn't come from the payments made.