Another advantage of having an open spot is that it makes going on hiatus so much easier, because when you come back, you can check if all your villagers are still there before starting your game. When you don't have a 4th character, if you went away unexpectedly and didn't deny a request to move on your last day, all you can do is go back to the day you last played and go through the whole process of getting someone to ping.
However, if none of the advantages of having room for a new character are that important to you (and most of them, other than checking to see if anyone's missing, probably don't matter to someone with a full set of 10 villagers), then you should do it. It's more room for items and patterns, another house you can decorate, and it helps complete your theme.
If you want to complete your theme but don't want to start a new character, maybe you can delete or change one of the existing ones.

I wanted a fourth character too until I found a way to combine one of my existing ones with that fourth character's theme.