This is intentional.
None of the culture-producing buildings that the previous civ built are there anymore. You'll have to fill in your own temple/cathedral/library/university/etc. if you want to produce your own culture in there.
Any wonders that you may capture will not give you any culture. They only give a culture benefit to the civ that built them. They may still be useful, though I would personally raze any city that has an obsoleted wonder in it (Oracle, Hanging gardens after steam power or Colossus after Flight, etc.).