The tax system would have to deepen deductibility for donations to devolve welfare's work to charities. A third-sector system could be created consisting of charity banks to manage the funds, or to grant the funds to charitable orgs. Churches and charities are too susceptible to fraud, usurpery and corruption. Probably more so than the government's system. Maybe that 3rd sector could help with that.
The government also tracks constituents, and has better access to tax info etc to make sure needies are really needy. Fraudulent needies can also spend their days going from charity to charity, so there will have to be a private system of tracking individuals' activities in the charity-space. Who would like that type of private tracking? Not all charities would even dig participation/administration on such a tracking system. Lord, if you thought exploitation of welfare among illegal immigrants is bad with the government administrating this...
Lots of big holes in the chances for this charity based welfare thing.
It would be a shame to see charitable dollars shifting to the private social safety-net sector and away from Jerry's kids and the WMKeck foundation, etc. If all charities were offered equal deductibility, the safety-net charities would probably struggle for funds... struggle for mine anyhow.
The biggest dividend of welfare is that it does add demand into a sweet-spot in the economy. That spot will suffer, taking the economy with it. Freedom to select goods within the market would be expressed by charities instead of needies, and probably at the wholesale level... potentially at the irregular/out-of-date level. Needies would probably end up eating what they're given and wasting what they don't care to consume. Needy kids would get toys they didn't want more often.
There's probably more to this, but I would go after the welfare state differently. This seems like a good-sounding proposal until further review. It sounds like a recipe for an africonomy: fraud, corruption and charities. I don't see a total devolution either. I don't see a change in consciousness between the welfare constituent or charityfare constituent, moreover.
Antagon policy rating for charities running welfare: 2.7 of 10.0