I don't actually advocate cutting disability pensions, but feel like playing devil's advocate anyway, so here we go.
The market for private charity is huge, and in the US alone something like $270b a year is donated. I don't think it's controversial to say that this would increase substantially if taxes were cut by a large amount (as they would be if the welfare state were stripped back). Additionally, private enterprise has almost without exception been better at allocating resources in other sectors of the economy than the respective government departments, and so it's not too much of a stretch to postulate that a private charity would be better able to provide for the most needy, while weeding out the cheats, than the current system. On top of this, if a private charity were revealed to have a large amount of people who probably don't need charity, or who could find a job fairly easily, leeching off it, donors would be much more likely to forsake that charity and instead donate their money to others.
The final benefit is that voluntary donations are ALWAYS preferable to forcibly extracted ones, and the latter describes the current system because it is based on taxation.