If someone making the median income in a city can afford a median house with 21% of their gross income, yes, I deem that "affordable."

To go back to my example, the family making $41k net annually is paying $10,800 (ish) annually in mortgage costs. They pay an additional $4,781 in property tax annually. That leaves $25,419 annually or $2,100 monthly for other costs and savings.

My example makes plenty of assumptions that won't necessarily hold (after all, I'm assuming averages here). Notably, I'm assuming a 20% down payment and excellent credit. And no, that's not a lavish lifestyle. But it's well within the realm of "affordable" for an average person.

I'll also note that $228,000 is the median price, but a search on Zillow shows >1500 listings for less than $150,000. I saw one listing for 3bd/2ba at $135k within the loop. near decent schools and within 20 minutes driving distance of downtown, the USAA and Valero corporate campuses and the UTHSCA medical center, all major employers.

I don't really see what your example has to do with my point. Yes, Austin is more expensive than SATX. Yes, someone making $51k should not pay $1600 a month in housing cost. But you're making my point for me—housing costs in medium-large cities are not necessarily out of whack average incomes in all such cities, just some markets (like Austin).