It depends on your town and if such a villager is vital.
My first town, Applewin, has three villagers who were there on Day #01: Jambette, Scoot, and Twiggy. I haven't allowed any of them, whenever stating an intent to move, to go because I am loyal to them. Those three, plus Kidd (who is slotted No. 10 on my on-screen menu list; he was from the Campsite), are a part of my vision for Applewin being a lovely town with some down-to-earth villagers mixed in with some superstars. (Those superstars are ones we find on
Bell Tree Forums member Hound00med's list among the top draws.) The more time having gone by the stronger the bond. So, I have used other slots to do some rotating of the cast of villagers in Applewin. (I most recently welcomed Hamlet. That Jock hamster is beautiful. He's cool!
Pics are below.)
I won't get into how I have managed other towns; but, I think it's wise to have a various reasons concerning with villagers to keep, and which ones to let go, because it may be a good personal balance for having a town more which feels
personal. Personally yours. You get a sense of which villagers should be there. And it also allows you, as you let some villagers move, to branch out and experience some new blood.
In a way…you end up
knowing when it's time to make a change.