^ I thought the reference was to The Clash song!
If you like that town, you should keep it and don't have to keep cycling. You can just get villagers to move at slower rates or use methods to move out villagers faster while keeping the ones you do. I think you should do what makes the game more fun for you, and it sounds like that might be keeping those villagers.

I wouldn't choose cycling over that, especially because I've noticed lots of people getting burnt out on cycling. You can still have villagers move in and out without cycling and while still stopping to enjoy your game.