You've forgotten to add the effect of automation on prices. Suppose you automate away half the jobs at a factory, saving half your wage bill. Given that manufactured goods are a highly competitive industry, your increased margins are hardly likely to last, so the increase in profits gets competed away. That means that the labour cost saving is being passed to consumers: that's how the "profits" (that is to say, lower prices) flow to consumers.
So in the limit, if all the jobs are replaced by robots then the goods should be priced at the cost of the materials. This is still too high for someone who doesn't make any money.
This makes no sense. If consumers are the bottleneck, then who's buying to create the taxable profits in the first place?
If things continue to head in the same direction, this is where we'll end up. Fortunately there is still time to increase the taxes on things like capital gains or high bracket incomes. Ideally we would have more asset taxation since income tax largely is spent on protecting American assets. (Some assets more than others.)