I can't imagine buying anything built after 1950.
My house was built in 1925. It's been through hell and it's still standing! All of that shoddy new subdivision construction can't hold a candle to a sturdy old house with real wood floors, plaster walls and ceramic tile bathrooms.
My .02
While I agree, those types of houses that are around here are few and far between. The few that are, are either ruins or way more than we can afford. The area where we live (and we do like the area) is suburbs. Just north of Houston. Not much history out here.
My wife grew up in one fo those types of houses. A large house that was built in 1928. The construction was much as you describe. It is located just outside of downtown Austin, TX. Her parents sold it for 750K and it has been put back on the market after some modernization (that makes my wife sick) for a touch over a million. That is a bit over our 140K price ceiling.
I can't imagine buying anything built after 1950.
Asbestos rules!