We don't 'need' cheap labor but the constant strive for more profits means that the company that uses cheap labor will out-compete the ones that don't so that everyone needs to.
Another thing about Robots. Let's say you could buy a robot to clean your house for $250k, or pay a cleaner $10/hour, which would you go for?
The robot might be cheaper for cleaning a large enough house (that would require 40 hours a week for a cleaner) over a number of years. Maybe if the robot cleaned 3 such houses on rotation it would be worth it. But for most people that capital expense is hard to bear.
For many people a robot is too expensive to invest in - they don't have the cash at hand, but labor they can pay per hour and get going right away with little upfront expense.
Robotics and automation won't take over any job anytime soon. There are far better alternatives for capitalist to make money without investing so much in R&D.
Today we're pushing more automation than before because it started to be expensive in some countries to build products (eg: China is far more expensive than before now) or find cheap labor.
We gonna have a wide and diffuse automation only when the middle class is a thing all over the world. Until we have wide economic disparity will be always cheaper to hire foreigners and cheap labor from underdeveloped countries.
A few examples: in Japan robots are a thing more than in westerns countries because their immigration policy is so strict that is very hard to find cheap labor from other countries or provide them a visa. So they need an alternative for jobs that nobody else want do (nursing)
US and Europe don't have this issue because they can afford to have immigrants from Mexico, Philippines, other countries (for the first) and Africa, eastern Europe (for the latter) that can take over the jobs that locals won't do anymore (nursing, constructions, low paid jobs in general).
In the end, full automation will be very hard to be accomplished in a capitalist society. More robots less jobs, less job more unemployment, more unemployment less money, less money less consumerism, less consumerism less profit, less profit less R&D, less R&D more cheap labor. The system will be hard to be adjusted, even in the best case scenario you might have one individual running an entire industry Not really the best for competition. We already have monopolies in the new economy, with automation might be even worst if regulators are not fixing the issue.
Nice straw man you've got there.