You do not need huge fingers to get around a wider Precision neck. I don't have huge hands and I played wide Precision necks only for years with no problem. I think people can talk themselves into being scared of a wider neck but it's really not bad at all. I have seen tiny tiny males and females playing full width Precision necks.
Oh, i meant the other way around. Fingers too big to "fit" on a jazz neck.
I don't think having a neck too wide is a huge problem. People do play basses with 5+ strings as well, after all.