Do robots pay taxes, work, or make new robots? No humans left. No robots left. No cows left to milk. No more need for government officials. Everything stops.
The argument against robot automation is the same argument against machine automation. Historically machine automation did cause pockets of unemployment, but the economy eventually adjusted and standard of living was raised for all.
The question is: "Will the convergence of AI and robotics result in labor dislocations so great that it breaks civilization?
Peter Drucker decades ago foresaw a "dream economy" where labor was focused on entertainment and imagination and less on physical labor.
Do robots pay taxes, work, or make new robots?
Entirely possible, yes, and yes.
Robots can certainly be taxed in a number of ways. They could be a assigned a tax classification where the owner has to pay some amount to operate the robot. Not much difference than the property taxes that businesses have to pay now on equipment. Taxes can be and are already applied to equipment sales and leases.
Robots certainly work. But they do not receive a wage or salary. Instead their creator/owner either rents them out or sells them. In that sense they are slaves. It's the slave owners that pay taxes. Either robots are taxed as part of production similar to income tax or sales taxes fund government. If they are producing more product, then maybe taxes go down.
There is an argument that income taxes are far more stable than sales taxes that are subject to waves of consumer sentiment.
And absolutely robots can become self replicating and AI can even be employed to evaluate and improve the robot design over time.
AI could have a number of different objectives. Design robots that are very effective for certain tasks. Design other robots that are very general purpose. Design some that can emulate humans, using tools designed for humans. Design some that are extremely safe to work in proximity of humans. Design some that are light weight for air travel. Etc.
"No humans left. No robots left. No cows left to milk. No more need for government officials. Everything stops.
Not necessarily. The rise of robotic tech doesn't necessarily eliminate humans any more than machines did.
There is one scenario where the economy adjusts and people find new employment in areas that aren't automated. Arts, sciences, and finding new ways to employ robots.
There is another where the majority of Earth's inhabitants are thrown out of work, governments are too slow or ineffective in their response, and wars and rebellions consume the planet.
There is another where robots either become sentient and decide human's are in their way. Or they implement a poorly design goal, such as eliminating human infections of malaria by eliminating all humans. A strategy of keeping human's safe and aiding humans must be part of the AI goals. Or humans have to find ways of remaining in control.
As long as humans exist, there will be cows and government officials. Everything continues.