The welfare state wasn't founded "to pay people to remain poor" as you put it.It was founded to provide a safety net that would hopefully help people to escape poverty or at least alleviate their conditions.
GO's real term cuts in benefits,while a clever political ploy,will cause hardship for hundreds of thousands,if not millions.
You are still not engaging with the substance of the issue. The welfare state was created as a safety net from which people would hopefully escape, I entirely agree. The problem is, that increasing out-of-work benefits by more than wages results in the safety net at the same height, or in some cases above, the first rung of the ladder.
This is the fundamental point. If people are better off on benefits than they are in work in simple cash terms then what is the incentive to look for and get a job? If you increase benefits faster than wages are increasing then that incentive to find work diminishes. That is what I mean by paying people to remain poor. Out of work benefits became (and largely still are) a cage from which people could not escape because they could never get employment that made them substantially better off. They were effectively being paid to stay out of the labour market.
The cost of living is a problem for everyone at the moment. That doesn't mean that it is right to limit public sector pay to 1% in order to subsidise rises in benefits for those not working.