The crossovers probably cost so much because they're underground and require extra tunnel space. (They require extra (as in between the two-or-more tracks that are being switched) foundations above ground too, which is probably more expensive than the switch itself.)

However, I'd like to see a cost breakdown.

Even the busiest lines in Tokyo are mostly single-rail. Of course, when a train breaks down, then nothing can happen, but at least you don't need 4 sets of rails, only 2 (one for each direction). There's probably way less in terms of delays because of that too. Each train is on its own set of tracks, so little cross-cutting.

But aren't most of the train lines in Tokyo owned and operated by separate competing companies They don't have to interoperate or not that much correct?

Once upon a time the trains in New York City were also owned by separate competing companies, there was the IND, BMT, and the IRT but they now operate as one entity under the MTA. As a result all these lines were originally built differently with different tunnel widths and platform to accommodate the different size cars. I think this level of interop adds to the complexity of the system as a whole.