If at all possible, I'd like to see lots of operator actions/interactions. Some of us seem to forget there is someone holding the PET, doing stuff. In the battle network games you weren't just Megaman, you were Lan. I don't know if there was a 50/50 mix but they took the chance to tell both sides of the story.
Afterall, it wasn't just the navis or net entities that were causing trouble, it was usually some jerks/evil orginazation trying to do this and that or trying to get their hands on something. The net was kind of a neutral tool, just there for use. It was the people who chose to break it or wield it like a weapon against others that sort of drove the story forward and forced all the groups (law enforcement, R & D, etc) to evolve and step up their game.
I realize that, if done improperly, a game with full-on operator time can have... pacing issues in the story, but it seems logical to do like they did in battle network and use the operator as a plot device to get the hero into the next network by accident or intent, and maybe help out in strange times where the network is inexplicably linked to the freakin' school light system, for example. Or for some godawful reason you have to fan/cool your PET during a scenario to give the navi time to fight in an over/volcano/etc.
For anyone who hasn't played any of the battle network games, my memory is rusty as it has been a while, but I believe those things actually happened.