Most of the stringed instrument players I know (guitar, uke) who use a pick do so because they have issues with growing their fingernails. I asked one guy how he played arpeggios if he always used a pick, and he said he just didn't.
The best player I watched perform used both a pick and his fingers interchangably. He would lick his picks and stick them to the body of his guitar so that he had several lined up. He would play a passage with his fingers and then grab a pick, use it for a few minutes, then just let it fall to the floor when he started using his fingers again.
A music store employee told me that ukulele players don't use picks when I asked if he had any leather picks. He then used that as an opportunity to pick up a uke and start strumming some tune. I told him I didn't care what ukulele players did, and please tell me whether or not he could sell me them item in question. He got irritated. As usual, I wasn't cool enough so my wallet & I left. He really showed me.
Personally, I don't use a pick because most of what I attempt to play requires both chord and fingerwork. That's probably just another way of saying I'm not talented enough to use both, or quick enough do what I want with a pick.