A lot of the price difference between Europe and USA now are wages. US wages for construction workers in NYC or SF are 2 or 3 times that of Madrid. Lots of things are cheap just for this reason alone.
Total compensation in the U.S. construction industry is about $46/hour on average: https://www.bls.gov/news.release/pdf/ecec.pdf. That's almost $92,000 for a 2,000-hour year.
Your argument is then essentially that people should be working indefinitely.
Also, a shared apartment costs as much as you say. Not a room (source: idealista.es).
Purchase prices are high, but I'm curious as to what you consider a bad neighborhood, given the overall safety statistics in Spain, and Madrid in particular.
Housing affordability is a real problem, but misrepresenting data is counterproductive, as it can be easily disproven.
The average salary refers to those who have a job. Most family units have some that don't.
I can't confidently say whether one feels more comfortable working construction in a globally VHCOL city like NYC or SF or in a MCOL city like Madrid.