I would have never written any code for class if given that option.
In the real world, you do get punished if you need to program something, but don't know how to. College CS classes aren't meant to teach you how to get stuff done using software, they're meant to teach you how to program. Handing in someone else's code is not going to accomplish that.
My CS course allows to use of others code, given proper attribution, but you only get marked on the stuff that you yourself contributed - if you were to take other people's code all the time you'll get pretty bad marks.
I think that works as enough of a deterrent to what you suggest whilst allowing students to get on with making interesting projects and not reinvent the wheel.
In the real world, you do get punished if you need to program something, but don't know how to. College CS classes aren't meant to teach you how to get stuff done using software, they're meant to teach you how to program. Handing in someone else's code is not going to accomplish that.