I have so many amiibo cards that I just use them most of the time. In NH I was TTing and using amiibo to get the villagers I wanted, essentially right when the game launched. I kept one plot at a time to keep cycling using NMT to see the new villagers. I specifically wanted Audie, Raymond, and Judy. To be honest, in NH I'm very controlling of who I let live in my town, but I wasn't always this way. Back in New Leaf I made sure to keep a few villagers I was particularly fond of, specifically Shep, Punchy, and eventually Ankha, Merengue, and Julian. The rest of the village I would just let cycle. Eventually I got into amiibo cards and had a town full of wolves.
That being said, I think letting your entire town cycle out and never using NMT sounds like fun too, you may even find a new favorite villager. It would be an interesting experience to never stop villagers from leaving.