Sadly, I have. In my repertoire it's only a handful, but without a pick they just don't work.
The most obvious ones are Summertime Blues and C'mon Everybody, but I can't get Let's Dance or Down Down to sound right with fingers either.
For pick playing I don't use the traditional thumb + forefinger grip, instead I use thumb + first two fingers. It's clumsy and restrictive, but you know exactly where you are and you're much less likely to drop the pick.
@BassAdder60 is spot on with the whole 'anchoring your hand' thing. With my r'n'r band I play a Precision with '57 pickup cover in place, so I rest the side of my hand on that and pluck between pickup and neck. With my covers band I play (mostly) a Rick 4003s5 with a sensible bridge so I rest the side of my hand on that and pluck over the bridge pickup.