Have you tried building a new rail line? Hint: adding a runway to an existing airport or building an entirely new airport, is simple, cheap and easy by comparison.
and this couldn't be done even though no houses need to go. in comparison the big dig tunnels under downtown boston were constructed just fine (slow and over budget but done)
Inside the cities rail use existing Rights of Way or build tunnels. Much easier to build a tunnel under a city than demolish 10 sq mi of cbd.