In the Yankees' case they could definitely use Darvish, they don't have a lot of depth. Severino is great, Tanaka and Gray are solid but both have question marks/red flags and then there's not much behind them, although of course their bullpen is ridiculous.
The Dodgers really don't need Darvish, they have all kinds of pitching depth, but much like the Astros if they can improve one of their starters to one of Darvish's level and use the others as trade bait they'll do so, and they actually have the money to afford it.