Robots could produce these public goods more cheaply. It'd be in the interests of anyone getting taxed not to have to support this "workfare" which is a bunch of inefficient government spending. Welfare could work just fine. It's a more efficient solution.
I don't see why it's necessary to try and require people to work. There are already incentives to work, without government forcing anything.
1. The market rewards those who create useful things with economic benefits.
2. Those with economic advantages enjoy social advantages.
3. Working in something you are interested in is fun.
Work is overvalued, imo. Nobody on their deathbed says "I wish I spent more time at the office!"
It's because welfare is utterly hated by too many people. The problem with Automation-Induced Unemployment is that it legitimately puts skilled people out of work and keeps them out of work. But, welfare is still completely hated. You'll find that workfare isn't, though. Look at the political support national defense gets, you can have a serious glut, spending too much, and any individual soldier is still respected. Not so for welfare.
People having jobs is really much better for morale. People having jobs that produces stuff increases the rate of total wealth growth as well, and it maintains a tier of Creative Destruction. Even with AIU and welfare, the market will still under-invest in public goods.
I forward that it's massively more political palatable