I like surprises, so I let the game decide a few times. I got Rex, Hopper and Amelia. I wasn't too happy about Amelia, but she has grown on me, so she stays. I have a hard time letting villagers go. I wish I could, because there are so many that I would love to have. When the ones i'm not as crazy about ask to leave, i think " now's my chance", but I just can't do it. I love Ketchup, and have her amiibo, but she will probably never get to live in my town. It's so silly.
What if you gave yourself a time that it's acceptable to let someone go, to give someone new a chance? Like after you've had a villager for at least 6 months or something like that? You could even tie a time limit in with a goal, like getting their picture, or celebrating their birthday with them at least once.
I always would let villagers leave when they asked no matter what - although once I got Fang I knew that he will be the one villager I will never, ever let leave. But then I realized that there were some villagers I let leave that I really wish I hadn't, because I didn't spend that much time with them. Katt was my starting Sisterly, and she quickly grew on me and became a favorite, and yet I let her leave in May. I wound up really regretting that. Then I had Melba, and she was probably only around for about a month before she asked to leave and once again I said okay... only to end up being really sorry I hadn't kept her for longer. Most recently I had Audie, whom I got in November, and she left earlier this month. So I had her for about four months all together and yet I still wound up regretting my decision on letting her leave.
Looking at the villagers I have now, the only ones I had at the beginning of the year are Merry, Boone, and Celia. Merry I have had since March; she was my first Peppy villager. And I'm ready for her to leave, as she has been with me for so long now. It's been almost a year! But Boone? I got him a little bit after I had gotten Audie, and I'm not as attached to him, so yeah, I'm ready for him to go too. Celia definitely cannot go - I actually got her in late December, so I've only had her a few months, and her birthday is tomorrow, as is mine. My birthday twin! So I already knew that I wasn't going to let her leave until after our birthday, although she hasn't asked yet anyway. But the others? They're all newer this year, and I've realized that I'm just letting them leave way too soon. Now I'm planning on keeping them around for longer, unless they're one that I really don't care for that much for whatever reason.
And to get back on topic, I have also decided that the next villager I get will be one chosen by the game to fill in an empty lot. Right now I don't have a Lazy, but I'm wondering: does "the void" supercede the missing personality type on your island when filling in an empty plot? I guess I'll find out when that time comes, but wondering if anyone else knows.