It's hard to see how a welfare system can be created that doesn't discourage work, unless it also leaves people in genuine need with nothing.
If you pay someone not to work you reduce the incentive to work, even if only by reducing the difference between working and not working. If you could make $8/hour by working then a 40-hour working week means $320 of income. If the government gives you $100/week to not work, that effectively reduces the benefit of working to $220/week, or $5.50/hour. If the government gives you $200/week to not work you're down to $120/week or $3/hour.
Out of that reduced useful income you also have to pay the costs of getting to and from work, and potentially also shift from Medicaid to a private health insurance policy with considerations like deductibles and copays.
If people moving from welfare into work keep the welfare payments then it creates an incentive for people to lose their jobs for long enough to get welfare before going back into work. If welfare payments are reduced on a sliding scale it creates an effective income tax that disproportionately affects the people at the bottom end of the economic scale. If welfare is abolished completely, or tapered until it disappears completely, the system leaves people who are genuinely unable to work stuck with nothing at all.
There is an argument that welfare should be administered more locally so it's easier to determine the level of actual need but ultimately the sad reality is that if money is offered to people who are unable to support themselves it creates an incentive for the people who simply don't want to work to act as if they are unable to work. Another argument that welfare should be replaced with private charity has a certain amount of merit although the difficulty in differentiating between someone who cannot work and someone who simply can't be bothered, between the person who lost their job yesterday and just needs some help to find their feet and the person who lost their job nine months ago and really doesn't feel like looking for another one, remains.
For good measure when people may have moral objections to work that is lawful it creates complications. At one level that might be a Muslim who would consider working for a pork butcher to be unacceptable, at another level it might be a woman who refuses to work as a prostitute. Allowing moral objections to certain forms of work make sense in situations like these but as soon as that door is open it invites abuse from people who find something morally objectionable about every job they are offered.
