Sabrewulf brings up a good point. I would like to see moving NPC's again, but not unless they fit the environment they were to be used in. Castelia City is more or less a replica of New York City and given my experience living there, people are always in a rush and hustling past you. No respect, I tell you! The moving NPC's in Castelia City was sort of like a representation of that. It gave you the feeling like you were in a large and busy city just like if you were in NYC.
Should GameFreak choose to do that again, battling them would be a nice addition to the concept. It would be quite unexpected since you wouldn't know who you run into will want to challenge you to a sudden battle. Then again, doing so would be choosing to ignore the idea that all of these running NPC's are in a hurry to supposedly be somewhere ─ unless, maybe, they were simply passing through like us. In that case, I'd hate to be someone who's rushing to a Pokémon Center in that exact moment.
I'd actually like something like the news reporters in RSE again. You remember how they showed up in different locations to battle you? Well, what if we had NPC's we battled in earlier routes show up again in future routes. That's technically considered moving NPC's, right? Just not in the exact same way as the folks over in Castelia City.