It's never been intended as a cure. The idea is that it represents a safety net.
That is just one perspective on what the welfare State is, and unfortunately it is not the way the most vocal proponents of social reform see it.
Many people think welfare can be used to re-engineer society in various ways - for example, paying for more university places for minorities/women, increasing upward mobility, prioritising training on poor areas, building youth clubs, providing government jobs to artificially inflate the size of the middle class etc.
The way welfare is perceived, and the social ends to which it is deployed, can be complex. So for many people, and for many government projects, they are designed to "cure" various social ills rather than simply limiting themselves to a social safety net.
And just to clarify an earlier comment, I meant that no society in British history has been so generous in helping the poor, disadvantaged etc. Yet there has been no let-up in the left-wing criticism telling us how evil, greedy, selfish etc capitalism is.
We've given the "left/liberals" almost everything they asked for since the 60s - in many ways, they have been given even more. Yet where is the great society they so omnisciently predicted? Now they tell us we need to keep giving and giving, that the giving doesn't work because we are too selfish and greedy - there is surely a disconnect considering how much has been done to help disadvantaged people in this society - at what great expense it was done, for seemingly no avail.
Moderator Action: The last two paragraphs are an excellent example of how conversations get derailed. This goes for everyone, not just Ayn: please avoid broad generalizations about "the right wants this" or "the left wants that." These sort of comments are not conducive to a healthy discussion. Please avoid them. 
