In the realm of Pro Wrestling nothing is impossible. I would absolutely love to see this unfold on such a grand scale. However, there are currently many problems that could possibly arise from this and just as many that will prevent it. One of the main ones is that NJPW are supposedly not big on WWE. I wouldn't know this as a fact, but there very well could be immense amounts of tension. Especially coming from the loss of Styles and Shinsuke Nakamura.
New Japan and WWE had a working relationship back during the 80s, I'm not sure of the circumstances that led to it ending, but it did. A whole lot has changed in pro wrestling since then, obviously, and there are obstacles to overcome. I don't think New Japan would be adverse to working with WWE because that's only going to jack up the prominence of New Japan and possibly lead to a stronger audience presence here in the United States.
However, there are obstacles to overcome and one of those obstacles is the fact that there would be a [LOT[/B] of big egos involved. There will be a lot of "cooks in the fire", as the old saying goes, and it could lead to huge disagreements regarding how the storylines play out, who goes over in what matches, how they go over, etc. There'd have to be a good deal of give and take on both sides that can be volatile from the very beginning because, ultimately, the loyalties of all those involved are going to be with the companies who're ultimately paying them; WWE's bookers are going to be loyal to WWE and New Japan's will be loyal to New Japan, so even if it's just from a storyline perspective, someone would have to come out on the "losing" end of this program and I very, very, very much doubt that Vince McMahon is going to roll over for anyone.
Another potential problem is that, as has already been mentioned, WWE doesn't really have anything to gain out of such an arrangement. WWE shows in Japan draw big crowds, the tours are profitable, there are quite possibly as many WWE Network subscribers in Japan as there are for New Japan's own streaming service, New Japan Pro Wrestling World. last year, WWE's revenue was fairly close to the $700 million mark, more than at any other time in history, whereas New Japan's revenue is maybe around $30 to $35 million. To be quite honest, WWE doesn't need to work with New Japan or anyone else.
It'd be pretty cool to see of course, but I don't see how it'd make much financial sense for WWE and that's what it's really all about at the end of the day.