Let me start off by saying that every American promotion needs to a partner with a regularly tour Japanese promotion. This is the greenest generation of wrestlers ever, we have 10 year vets who have had less than 600 matches. Practice makes perfect and unfortunately Japan is the only place that can provide space to practice.
WWF worked a lot with Inoki, and AJPW worked with the NWA. However, Bruno liked working with Baba, and being the WWF got, got to work with All Japan instead of new Japan.
In the 90s WWF switched over to Super World of Sports, a start up by a glasses company that was throwing way too much money around. And WCW linked up with New Japan. After Super World of Sports failed I don't think WWE worked with Japanese promotion outside of booking TAKA and Sasuke and sending Undertaker to a one time appearance in Michinoku pro.