I think there are other less impersonal, more policy driven reasons than robots why the middle class is being hollowed out, but it sure feels like they'd rather we believed it was robots.
It turns out financial limitations are the easy factor to solve. Other, non-financial limits to social mobility are so much more stubborn.
The only requirement is to pass the entry exams, which anyone can take
[0] https://statisticalatlas.com/place/Texas/Austin/Household-In...
You're comparing household income to individual income. If you look at individual income, $100k/yr in Austin is much going to be much higher than 80th percentile.
I don't think that's a good definition for the middle class. There's strong support for the fact that income distribution is an exponential distributions - just google "income distribution exponential".
A exponential distribution is not symmetrical, so its mean or median is not a great centrality measure, it does agree with intuitions developed from observing, say, a normal distribution (like the weight or height of persons). The mean or median are very far from the mode (the most frequent individual) in an exponential, whereas they're almost identical in a normal.