I voted "I do," though it really depends on the town in question.
My main town is loosely themed. The three side characters and their houses are fully themed, but I--the mayor--and the villagers are not. These villagers are a mix of old and new favorites.
AHS is fully themed, and every one of its villagers shares a name with someone from American Horror Story. (This is my only town in which every villager was chosen because of theme.) This worked out pretty well, since I am now fond of villagers I wouldn't have considered before, such as Del and Queenie.
Goblin is fully themed, though only three of its villagers (Shep, Roscoe, and Muffy) were chosen because of the town's theme. Even then, I really like all three, and was glad to have them. The rest of Goblin's villagers range from starters who grew on me (Tammi) to my absolute favorite villager of all time (Mallary).
My in-progress town is also themed, and its villagers all fit the theme but are also ones I'd love to have anyway. Same with the plans I have for, like, six other towns.
The main thing for me right now is trying not to have repeat villagers in my multiple towns.