People aren't likely to buy a typical middle class home as their first house, they'll usually start in a starter home/townhouse and then upgrade as their family gets bigger. By that point, their house will have appreciated and they'll have built some equity, meaning they can afford a larger house than if they had been renting.

So while the math may be correct given the inputs, I think the inputs don't make sense for most people.

It's probably okay to stretch a bit (say, 40-50% of income) on the first home, since income will likely increase and the payments will stay mostly flat. Just don't expect to buy a new house, new car, and new furniture all within the first 5-ish years.