There are two different ways to look at pay, imo: What people deserve to get paid, and what rates and benefit packages are needed to attract the best people to the job - particularly when the demand for a particular skill set, experience and competency exceeds the supply.
The former is subjective, the latter is more objective.
I think that care work should be paid much better - not just because they deserve more ( they do), but also because the rate at the moment isn't high enough to attract and retain enough people.
Care worker's pay is not connected to how much the top rung of civil servants get paid though. Paying those at the top less won't help care workers. The problem with the best paid public sector workers, is that even if we might not think they "deserve" their high pay, if their skills are in high demand in the private sector then we need to offer them something to keep them within the public sector. "Deserve" has nothing to do with it.