Welfare is much bigger than EBT. There is Medicaid, Rent subsidies, Heat subsidies, Obama phones, free internet, free legal services, free transport to hospitals, free lunch in schools on and on. I don’t think EBT card can be used for all those benefits.
In many States, illegal aliens manage to access all of those benefits ... either without ID, or with fake ID ...
You’re actually starting to develop the argument that voter ID requirements are useless. I’m not there yet, but it’s certainly a potential problem.