A Shohei Ohtani trade to the Yankees won't happen because it'd involve doing two things they've refused to do
The New York Yankees are one of the most storied franchises in the history of sports. They have 27 World Series championships, and make the playoffs virtually every year. While that still holds true to this day, they're operated in a different way.
George Steinbrenner doesn't own the team anymore, his son Hal does. While George used to stop at nothing to win right now, Hal isn't the same way. The Yankees don't spend the way they used to, and they don't trade prospects the way they used to.
The Yankees do have a very hefty payroll thanks to an active offseason, but were reluctant to pass the fourth luxury tax threshold. Trading for Ohtani and his $30 million salary would take them well over that mark. In any Ohtani trade, there's almost no chance that the Angels take money back, so the Yankees would have to find some other way to clear money. In other words, it won't happen. Can they change their stance? Certainly. Will they? Who knows!
For years, the Yankees have held onto their prospects for dear life. Anthony Volpe has been as close to untouchable as any prospect in the game, the same goes for Jasson Dominguez. As much as Yankees fans don't want to hear this, an Ohtani trade won't be for their 20th ranked prospect straight up. The package will be a hefty one.
Will the Angels make them give up Volpe? I have no idea. Will they make them forfeit prospects they don't want to trade? Absolutely. The Yankees can wait until the offseason and try to convince him to go out east, but the Angels are the ones holding the cards here. Unless the Yankees are now suddenly ready to go all-in prospects-wise, it won't happen.