Technology has been replacing workers since the tractor was introduced around 1900. But unemployment hasn't kept going up because we keep finding new ways to employ people.
But if by some miracle we do finally automate everything minimum wages won't help at all - we're talking about a situation where there's no reason to employ someone in the first place. In that case just tax production and provide everyone a guaranteed minimum income. No need to worry about work disincentives, they weren't working anyways!
>But if by some miracle we do finally automate everything
or
If we quit finding new ways new ways to employ people...
You don't have to automate everything, just increase unemployment to a significant enough percentage and social instability (rioting, political unrest) will be the primary concern.
But if by some miracle we do finally automate everything minimum wages won't help at all - we're talking about a situation where there's no reason to employ someone in the first place. In that case just tax production and provide everyone a guaranteed minimum income. No need to worry about work disincentives, they weren't working anyways!