I don't think it is necessarily fair to blame Labour for the growth of the welfare state, I do think it started with Thatcher, as a means to massage shocking unemployment figures by moving people onto sickness related benefits.
I do not support Tory austerity, by any means, but it is hard to get a tiny violin out for people who continue having children with no expectation or means to support them financially.
It is easy to forget that the welfare state was established to fight 5 giants that were holding us back: poverty; disease; ignorance; squalor and idleness. I think that last one is often forgotten. Even at its inception, the welfare state was intended to fight idleness.
Sadly, it has lost its way and if anything now props up low wages and very part time/insecure jobs. People are usually happier and mentally healthier for working and earning, so we have to try and get people earning, not trapped in an endless cycle of child rearing, for their own sake and that of their children.
I prefer carrot to stick, so am not wildly in favour of the benefits cap, but the level it has been set at seems high enough to be reasonable. However, it should be combined with proper training support to get back in to work and young people need genuine opportunties where they can see a way to make a life for themselves before becoming parents. Nothing reduces the childbirth rate like women's access to education and opportunities.