I've often thought it would be novel for the champ to come out first. Hog the limelight as long as he wants, get the home crowd to make it intimidating for the incoming opponent, etc. You could certainly make it work by choice if you were as dominant as Inoue - "come in, if you're hard enough" etc!
Think it’s the custom there, for the champ to go in first. I’ve noticed that in several Japanese shows, apart from the recent Inoue fights.